Category: Physics Notes PPT

Lux is a unit of illumination which is in the International System of Units that is SI. One lux Latin for “light” is said to be the amount of illumination that is provided when one lumen is evenly distributed over an area of one square metre. This is also said to be equivalent to the illumination that generally would exist on a surface all points of which are one metre from a point source of one international candle or candela. One lux is said to be equal to 0.0929 foot-candle. In this article we are going to discuss a few more things related to this topic lux.

Lux Definition

The lux which has the symbol: lx is the SI unit that is derived from illuminance measuring the flux luminous per unit area. The lux is said to be equal to one lumen per square metre. In photometry this is used as an intensity measure. This is so because it is perceived by the human eye of light that hits or passes through a surface. It is analogous to the unit that is radiometric watt per square metre.

But with the power at each of the weighted wavelengths according to the luminosity function there is a standardized human model visual brightness perception. 

In English,  the word -“lux” is used as both the singular and plural form.

The word is said to be derived from the Latin word that is for “light”,- lux.

The power per unit area on a surface that is  illuminated and sometimes known as areance is distinguished from the similar quantity for the source. 

In radiometry the areas of the surface may be known as irradiance and luminous areance may be known as illuminance. This is the importance in the practical quantity  in judging whether an area is lighted well enough for reading or other activities. The illuminance is said to be measured in lux. 

But the unit that is the older one is the footcandle which is still encountered.

The lux is defined as a lumen per square meter and lux is said to be a unit of illuminance. A term which is more equivalent is luminous density of flux.

As such, we can say that it measures the amount of visible light striking a surface. The standard symbol for it is Ev. We must take into account the sensitivity of the eye for the wavelengths of light which is involved in this. But that is taken care of in the establishing the lumens number.

Lux Light Measurement

We are going to understand this by performing an experiment. For performing this experiment we require:

• Any Smartphone or tablet with internet access to it and permission to download and install an app as well.

• A surveillance of adults that is to help verify and download the app.

• There should be different light sources that are the flashlight, lamp, ceiling light, etc.

• It should be a different location that is a dark closet, room with windows, outdoors, etc.

• The ruler that is optional.

Preparation of the Experiment

• We can ask an adult to help us search for a “lux meter” or we can say a”light meter” app on a smartphone or tablet. There are many free options also which are available please note that some apps which might have ads or in-app purchases enabled.

• Then we get to know our lux meter app.

Procedure to Follow

• We will test how lux readings change with distance from a fixed source of light. For example we can directly stand under a ceiling light. And we can hold our phone with the screen facing up and move the phone up and down for a time being. 

• Now we need to alternatively hold the phone and sideways and aim it toward a floor lamp as you walk closer to and farther away from the lamp. How do the readings change as the distance changes?

• Now we need to compare different lights which are the artificial sources of light at the same distance. We  can even use a ruler for this or any convenient object or a body part such as our forearm as a spacer.

• The exact distance doesn’t matter until  we keep it constant. Now we can ask a few questions that are how does a flashlight compare with a light bulb? What about the light which comes from a TV or computer screen? What light source in our house is the brightest? 

• Finally now we can measure ambient light levels in different locations. We need to turn off all sources of artificial light and measure the same way which is mentioned above. 

The Observations and Results

We  probably will notice how dramatically lux changes with distance from a light source. We  might only read a few hundreds or tens of lux when we are across the room from a light bulb. But originally if we hold our phone right up to the bulb, then we can see that the reading could be in the thousands or even tens of thousands. This is because of a mathematical relationship known as the inverse square law. 

As the light expands outward from the main source the amount of light which is hitting each area drops off very rapidly. The sun is so far away we might find it surprising that the reading of lux in direct sunlight is so high that it goes in the tens of thousands of lux. This gives us a sense of just how very bright the sun itself is and this way we can measure light also.

Magnets are magnificent objects that create an invisible area of magnetic force around them; this area is known as the magnetic field. 

When an object is brought near to this field, it gets attracted to the magnet without any physical contact. So, magnetism is the property of an object of getting attracted to the magnet.

On bringing the N-pole of two freely suspended magnets together, the two magnets repel each other; however, on reversing the direction of one magnet, both magnets attract each other.

Materials like nickel, iron show magnetism, while materials like wool, cotton don’t.

What is Magnetic Force?

We know that the current in the conductor is due to the motion of free electrons in a definite direction. When such a conductor/wire is placed in the magnetic field, each electron moving in this field experiences a force. Thus the current-carrying wire/conductor experiences a force in the magnetic field.

Now, let’s say a charged particle with velocity ‘v’ is moving in a magnetic field ‘B’. Because of the interaction between the magnetic field produced by moving charge and the magnetic field applied, the charge ‘q’ experiences a force called the magnetic force.

Magnetic Force

Now, let’s understand how to find magnetic force.

Let’s suppose that a positive charge ‘q’ moving in a uniform magnetic field Bwith a velocity [overrightarrow{v}]. The angle between [overrightarrow{B}] and [overrightarrow{v}] is θ The force experienced by this charged particle depends on the following factors:

• The magnitude of the force experienced by the charge is directly proportional to its magnitude, i.e., F ∝ q….(1)

• The magnitude of the force [overrightarrow{F}] is directly proportional to the velocity component [overrightarrow{v}] acts in a perpendicular direction to the magnetic field, i.e.,

                       F  ∝ v Sin θ…..(2)

                      F ∝ B….(3)

Combining equations eq (1), (2), and (3), we get:

                                 F ∝ q B Sin θ

Now, removing the sign of proportionality constant, we get:

                        F = k q v B Sin θ

Here, k is a constant whose value is 1, so the equation becomes:

                  F =  q v B Sin θ

                [overrightarrow{F}]       = q ( [overrightarrow{v}] x [overrightarrow{B}] )

Definition of [overrightarrow{B}]

If v = 1, q = 1, and Sin θ = 1,then:

          F = B

It means that the magnetic field induction at a point on the magnetic field is equal to the force experienced by the unit charge moving with a unit velocity in a direction perpendicular to that of the magnetic field at that point.

Now, we will look at the special cases on determining the direction of magnetic force:

Direction of Magnetic Force

We can see that the direction of the magnetic force is the cross-product of velocity and magnetic field, which is perpendicular to the plane containing [overrightarrow{v}] and [overrightarrow{B}]. 

Let’s consider a piece of paper where [overrightarrow{v}] and [overrightarrow{B}]are in the plane of the paper, then according to the Right-handed screw rule, the direction of [overrightarrow{F}] on the positively charged particle will be perpendicular to the plane of this paper upwards. However, on the negatively charged particle, the direction changes to downward. 

We can see the visual representation of the right-hand screw or right-hand rule for both positive and negatively charged particle below:  

(Image to be added soon)

Special Cases on Magnetic Force

We know that the equation for the magnetic force is given by:

             F = qvB Sin

Now, we will consider the following cases by taking ‘‘ as the variable here:

Case 1:

If θ = 0° or 180°, then Sin θ= 0

From the above equation, we get F = 0. It means a charged particle is moving in a direction parallel to that of the magnetic field. At this moment, a charge experiences no force.

Case 2:

If θ = 90°, then Sin θ = 1

From the above equation, F = 1

At this moment, a charged particle is moving in along a line perpendicular to the direction of the magnetic field. At this moment, a charge experiences a maximum force.

At times, when a charge experiences a maximum force, the direction of the force can be determined by Fleming’s left-hand rule. Now, let’s understand what this rule says:

Fleming’s Left-Hand Rule

Fleming’s left-hand rule is applicable for a special case when a charge experiences a maximum force. 

If we stretch our first two fingers and the thumb, where the first finger is an index finger while the second one is the middle finger. 

The index finger, central finger, and the thumb lie perpendicular to each other, and each of these represent a direction of a few things; let’s see what are those:

• Index/First finger – Represents – the direction of the magnetic field

• Central finger – Represents – the direction of motion of a moving charge (electric charge)

• Thumb – Represents – force experienced by the charged particle

If the velocity [overrightarrow{v}] is along the X-axis and [overrightarrow{B}] is along the Y-axis, then [overrightarrow{F}] is along the Z-axis. Below is the representation of this statement:

(Image to be added soon)

Management of natural resources refers to all those activities related to all renewable and non-renewable sources of energy. The management of these sources is important to maintain the balance in the ecosystem. Let us look at the reasons why the management of natural resources is necessary.

Mother Earth has bestowed us with several sources of energy. We need the energy to support different life forms on this planet. We extract different forms of energy from different sources. The natural resources present on this planet are the chief sources of energy for our daily activities. However, all of these natural resources are not renewable. Therefore, to ensure proper usage of each of these natural resources so that none of the sources faces any problems of getting used up, we need to manage natural resources. Let us learn more about the management of natural resources.

Why is Management of Natural Resources Important?

It is important to manage the natural resources available to us. The following reasons justify why we need to manage our resources.

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• Natural resources are needed to be managed to maintain balance in the ecosystem. All components of the environment are related to each other. An imbalance caused due to the over-consumption of these resources will disrupt this balance, affecting all kinds of life forms directly or indirectly related to it.

• Managing equal pressure on different sources of energy prevents overdependence on any particular source. Previously, people-based most of their work and technology on coal and petroleum. However, both these sources are non-renewable and give rise to several toxic substances and pollution as by-products of its consumption. Recent trends shift towards renewable sources like solar energy and hydro energy, thus lessening the burden on these non-renewable sources.

• We must allow our future generations to use such resources. We must not overuse any resource to such an extent that it gets depleted. If we do so, we are preventing our future generation from such sources of energy.

Need for Conservation and Management of Natural Resources

We have valid reasons to conserve the natural resources that we use daily. Let us look at the following points to validate this statement.

• Most of our activities are based on the use of natural resources. These resources are obtained from different sources. A significant fraction of our sources is non-renewable, meaning that it is difficult to replenish them once used.

• Rational distribution of pressure will enable all the resources to be used properly. More pressure must be exerted on renewable sources like solar and hydro energy sources. This move will also reduce the pressure on non-renewable sources. Moreover, several kinds of pollution can also be controlled by such management.

Now, let us discuss some of the important steps to resolve the issues of waste management in the form of 3 R’s:

The Three R’s of Waste Management

Waste management is a synonymous term associated with resource management. This is because waste generation and waste handling also require resource consumption. To prevent excessive use of resources for waste management, it is important to follow the three Rs of waste management- Reduce, reuse, and recycle. Let us look at each of them in detail.

(Images will be Uploaded soon)

1. Reduce

Reduce calls for smart management, purchase, and use of products. It is based on the principle that we will not produce much waste if we do not use resources. The best way to limit our usage is by:

• Avoiding the use of disposable products like paper plates and cups, plastic straws, and switching to reusable ones. 

• Checking for the durability of the product and settling for the better quality ones. 

• Prevent the use of plastics, and replace these products with the ones made from cloth.

2. Reuse

Reuse calls for using products that have been used before. Such a step will prove to be economical as well as environmentally friendly. The best way to reuse are:

• Reuse plastic and paper bags for different purposes.

• Donate old dresses, books, furniture, electrical appliances, etc.

• Reuse simple household items for other applications.

3. Recycle

Recycling is the process by which used products are transformed into new products used for different purposes. For example,

• People can use different DIY ideas to convert plastic bottles for different household needs, like pots for planting trees.

• Recycle the used paper products to make newspaper bags.

• Purchasing recycled products that can be recycled yet again.

Ways for Natural Resource Management

Natural resources comprises air, water, sunlight, Coal, Petroleum and natural gas, fossil fuel, oils extra. These resources are many times exploited by humans for economic gain. Some resources have the capability to renew but some are non-renewable. 

As humans it is our responsibility to conserve, protect and take care of our natural resources because it fulfills important and basic needs to live. Let’s discuss what role we can play in the management and conservation  of natural resources.

Following are the methods for the management of natural resources:

• Enhancing skills, capacity, and engagement

• Efficient use of alternative sources of power such as wind energy and solar energy

• To conserve water in our homes by practicing judicious ways

• Using pipelines for the transportation of oil as oil spills are highly detrimental to aquatic plants and animals.

• Proper treatment of sewages and industrial wastes before releasing them into water bodies.

Degradation of natural resources

Fertile soil is being lost at the rate of 24 million tonnes the year and one-third of the planet is severely degraded. Bad farming techniques such as heavy tilling, multiple sequential harvests and abundant use of agrochemicals are also a cause of degradation of natural resources.

The natural resources that you see around you are renewable and nonrenewable resources. Renewable are those resources that can be naturally restored over a period of time and nonrenewable are those that cannot be sustained in the same speed that it is being consumed. So, let us take some measures to stop the degradation of natural resources and also follow the steps to conserve it.

Here we are going to learn in detail about motion. To learn about the motion and rest we have to be aware about the reference point or stationary object. To mention the condition of any object we have to first recognise its reference point and stationary object. On the reference point, the stationary object does not change position.

For example, we can consider a building and a car, then a building will always be stationary because it will not change its position. Although cars can change. So, we can say that a car is in motion. we have to consider a stationary object with respect to it.  This stationary object is generally called a reference point.

Rest and Motion

Now assume a car standing in front of the building at any location A. Let’s say that  after some time it will be at location B. It means that it has changed its position concerning the stationary object that is the house and if that car keeps on standing in position that means it has not changed its position with respect to it. Here the building is at rest so with their help we can learn about what is clearly rest and Motion.

Rest: Rest is the process when a body does not change its position in a specific interval of time with respect to the surrounding or the considered reference point, then it is called in the position of the rest.

Motion: When a body changes its position in a specific interval of time with respect to the surrounding or the considered reference point, then it is called in the position of the motion.

So from here we can say that an object which is in motion or in rest has the following characteristics.

Characteristics of a moving object

The moving object is that, which changes its position with time. As we have seen, the movement of the car can be easily seen, that is, we don’t have to concentrate much. Because it covers a significant distance in a given period of time. However to know the movement of a needle of the clock hour hand we need to ensure it. This is because  motion of some of the objects is faster in comparison to others. So that we can see it happening.On the other hand,  motion of some of the objects is so slow that it can’t be seen undoubtedly.

In conclusion we can say that a wrist watch has three hands: minute, seconds and hour hand. Out of them, second-hand moves faster than others. So it is significant to observe. But to observe the motion in hour hand and minute hand we have to keep track because of moderately slow motion.

According to Newton’s first law of motion: A body tends to remain at rest or in motion until or unless an external force is applied to it. Therefore, on giving a push to a body, the body changes its position. So, the change in position of a body over time is called the motion. There are various units to measure the rate of change of motion of a body namely: Speed, average speed, velocity, average velocity, instantaneous velocity, etc. Here, the basic consideration for the measurement of rate of change of motion is time. Let’s discuss these units in detail.

Speed What do you Understand by the Term, ‘Speed’?

Speed of any body is defined as the rate of change of position of that body in any direction.

It is also defined as the distance covered by the body in a unit time in any direction. 

The formula for the same is given by:

Speed = Distance Covered / time taken  = D/T

Its unit is m/s in the mks system or SI and cm/s in the cgs system.

Types of Speed:

1. Uniform speed: An object that covers equal distances in equal intervals of time.

2. Variable speed:  An object that covers unequal distances in unequal intervals of time. It has a magnitude because the direction of the body is unknown. Therefore, speed is a scalar quantity.

Average Speed

When an object is moving with a variable speed, then the average speed of that object is that constant speed with which the object covers the same distance in a given time, as it does while moving with variable speed in a given time.

Average Speed Formula Physics

Average speed formula in physics is given by:               

Its unit is also m/s in the mks unit and cm/s in the cgs system.

Define Average Velocity

• Velocity of an object is equivalent to the rate of change of displacement.

• Where displacement is a vector quantity and is defined as the distance between the two positions of the object in a particular direction during a given time.

• Velocity is a vector quantity as it has both magnitude (speed) and direction.

• The value of velocity and displacement can be expressed as zero, negative or positive.

• The average velocity is defined as the total displacement of the body divided by the total time taken.

Average Velocity  (Physics)

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If you look at the above graph, there are two points A and B.

Here, the point A corresponds to time t1 and displacement x1 while point B to time t2 and displacement x2.

Displacement of an object at time interval (tᵣ – tᵢ) =  xᵣ – xᵢ.

The formula for the average velocity is given by:           

Where, 

              xᵢ = initial distance

              xᵣ =final distance

               tᵢ  = initial time

               tᵣ =  final time

If there are diverse distances let’s say d1, d2, d3….dn in different time intervals t1, t2, t3,…..tn     

Then, formula is given by,

The slope of a straight line AB is given by:                  

The eq(2) states that the magnitude of average velocity of the object between two points is equal to the slope of the straight line AB joining these two points on the graph.

Average velocity formula physics

  If   u = initial velocity

        v = final velocity

Then the formula for the mean velocity is given by, 

The average velocity equals the sum of the initial velocity and the final velocity divided by 2.

Instantaneous Velocity (Physics)

The word instant means at that very moment. 

So the instant velocity of an object in motion is calculated at a specific point(x,t).

This velocity is the limit of average velocity as the elapsed time approaches zero.

Since average velocity between two points A and B is

                                  Vav= xᵣ – xᵢ/ tᵣ – tᵢ

If time interval is small i.e., t2 -t1 = Δt and x2 – x1 =  Δx

 If Δt -> 0, the average velocity becomes instantaneous velocity.

Then,                       

Hence, instantaneous velocity of the object is the first derivative of displacement with respect to time. 

Do you know?

When a body is traveling through a uniform motion along a linear path in a given direction, the magnitude of the displacement is equivalent to the actual distance traveled by the body in a given time.

Types of Motion with Explanation

On the basis of nature of movement Motion can be classified into the following categories:

Linear Motion

Linear motion is the kind of motion where we move in a straight line is called linear motion. For example, driving on straight roads is an example of linear motion.

Rotational Motion

The rotation of earth can be an example of rotational motion. We know that earth rotates on its axis which causes day and night. Its progress is an example of rotational motion because it is rotating on its axis. Hence, we can define it as the rotational motion when the body rotates about a fixed axis.

Circular motion

The motion in a circular path is called the circular motion. All of us observe roundabouts on-road everyday. Also when we go through any road, we can’t go straight through it. We also take some curved roads and will also go through circular motion.

The movement of the body in a curved path is called the circular motion. one more example could be satellites orbiting around the planet.

Vibratory Motion 

Everyone must have seen someone playing the instrument guitar. So generally what happens when you hit it with your finger.The strings of the guitar vibrates and produces the sound. This motion is called vibratory motion. This motion happens due to the vibratory motion of particles. Hence,  motion is produced when the body shows to and fro movements.

Scalar and Vector Physical Quantities

We have learnt many of the physical quantities like velocity, speed, displacement etc. All these quantities can be classified under two categories. These categories are scalar and vector. It depends upon whether they provide the complete information about the magnitude  and directions or give the unfinished information like only direction.

Conclusion:

Everything and everyone around us are in motion most of the time. To understand the different types of motion is a hefty thing to do. This article explains motion, its characteristics, and types. You can peruse through this for a better understanding.

While studying crystallography, understanding crystal planes are of high importance. Miller Indices are the mathematical representation of the crystal planes. The concept of Miller Indices was introduced in the early 1839s by the British mineralogist and physicist William Hallowes Miller. This method was also historically known as the Millerian system and the indices as Millerian or the Miller Indices. 

The orientation and direction of a surface or a crystal plane may be defined by considering how the crystal plane intersects the main crystallographic axes of the solid. The use of a set of rules leads to the assignment of the Miller Indices (hkl) a set of integers that quantify the intercepts and thus may be used to uniquely identify the plane or surface. In this article, Miller Indices are explained in detail along with some solved examples for a better understanding.

Crystallographic Planes

We know that crystal lattices are the infinite array of points arranged periodically in space. These points can be joined together by drawing a straight line and by extending these lines in the three-dimension we notice that they appear to be a set of crystal planes or Crystallographic Planes. The crystal lattices are constructed by the set of parallel lines known as the Crystallographic Planes.

The lattice points have different mechanical, electrical, or optical properties in different directions, this will make the study of crystal structure difficult. To overcome this difficulty, we will choose a set of crystal planes such that the properties of the crystal lattice remain unchanged in the direction of the crystal plane. In order to choose specific crystal planes, a famous mineralogist William Hallowes Miller introduced a method known as the Miller Indices. Basically, Miller Indices are the mathematical representation of the set of parallel Crystallographic Planes.

Miller Indices Definition

After joining the crystal lattice points by straight lines, those straight lines were assumed to be the set of parallel crystal planes extending them in three-dimensional geometry. The problem that arose was the explanation of the orientation and direction of these planes. Miller evolved a method to designate the orientation and direction of the set of parallel planes with respect to the coordinate system by numbers h, k, and l (integers) known as the Miller Indices. The planes represented by the hkl Miller Indices are also known as the hkl planes.

Therefore, the Miller Indices definition can be stated as the mathematical representation of the crystallographic planes in three dimensions.

Construction of Miller Planes

Let us understand the steps involved in the construction of Miller Planes one by one. To construct the Miller Indices and the Miller Plane we follow the following method:

Step 1:

Consider a point or an atom as the origin, construct a three-coordinate axis and find the intercepts of the planes along the coordinate axis.

Step 2:

Measure the distance or the length of the intercepts from the origin in multiples of the lattice constant.

Step 3:

Consider the reciprocal of the intercepts. Reduce the reciprocals of the intercepts into the smallest set of integers in the same ratio by multiplying with their LCM.

Step 4:

Enclose the smallest set of integers in parentheses and hence we found the Miller indices that explain the crystal plane mathematically.

Rules for Miller Indices

• Determine the intercepts (a,b,c) of the planes along the crystallographic axes, in terms of unit cell dimensions.

• Consider the reciprocal of the intercepts measured.

• Clear the fractions, and reduce them to the lowest terms in the same ratio by considering the LCM.

• If a hkl plane has a negative intercept, the negative number is denoted by a bar (  ̅) above the number.

• Never alter or change the negative numbers. For example, do not divide -3,-3, -3 by -1 to get 3,3,3.

• If the crystal plane is parallel to an axis, its intercept is zero and they will meet each other at infinity. 

• The three indices are enclosed in parenthesis, hkl and known as the hkl indices. A family of planes is represented by hkl and this is the Miller index notation.

General Principles of Miller Indices

• If a Miller index is zero, then it indicates that the given plane is parallel to that axis.

• The smaller a Miller index is, it will be more nearly parallel to the plane of the axis.

• The larger a Miller index, it will be more nearly perpendicular to the plane of that axis.

• Multiplying or dividing a Miller index by a constant has no effect on the orientation of the plane. 

• When the integers used in the Miller indices contain more than one digit, the indices must be separated by commas to avoid confusions. E.g. (3,10,13)

• By changing the signs of the indices 3 planes, we obtain a plane located at the same distance on the other side of the origin.

Examples

1. Determine the Miller Indices of Simple Cubic Unit Cell Plane 1,[infty],[infty].

Ans:

Given that we have a plane 1,[infty],[infty] our aim is to determine the Miller indices for the given set of the plane. We know that we have a set of rules for determining the miller indices and they are as follows:

Step 1:

Consider the given plane 1,[infty],[infty].

Step 2:

Take reciprocals of the intercepts,

[frac{1}{1}], [frac{1}{infty}], [frac{1}{infty}]

Step 3:

Take LCM of these fractions to reduce them into the smallest set of integers.

1,0,0

Therefore, the miller indices for the given plane is 1,0,0.

2. Determine the Miller Indices for the Plane 1,[infty],1 

Ans:

Given that we have a plane 1,[infty],1, our aim is to determine the Miller indices for the given set of the plane. We know that we have a set of rules for determining the miller indices and they are as follows:

Step 1:

Consider the given plane 1,[infty],1.

Step 2:

Take reciprocals of the intercepts,

[frac{1}{1}], [frac{1}{infty}], [frac{1}{1}]

Step 3:

Take LCM of these fractions to reduce them into the smallest set of integers.

1,0,1

Therefore, the miller indices for the given plane is 101.

3. Determine the Miller Indices for the Plane ½,1,[infty]  

Ans:

Given that w
e have a plane ½,1,[infty], our aim is to determine the Miller indices for the given set of the plane. We know that we have a set of rules for determining the miller indices and they are as follows:

Step 1:

Consider the given plane ½,1,[infty].

Step 2:

Take reciprocals of the intercepts,

[frac{1}{frac{1}{2}}], [frac{1}{1}], [frac{1}{infty}] 

Step 3:

Take LCM of these fractions to reduce them into the smallest set of integers.

2,1,0

Therefore, the miller indices for the given plane is 2,1,0.

4. Determine the Miller Indices for the Plane −1,[infty],½

Ans:

Given that we have a plane −1,[infty],½, our aim is to determine the Miller indices for the given set of the plane. We know that we have a set of rules for determining the miller indices and they are as follows:

Step 1:

Consider the given plane −1,[infty],½.

Step 2:

Take reciprocals of the intercepts,

[frac{1}{-1}], [frac{1}{infty}], [frac{1}{frac{1}{2}}]

Step 3:

Take LCM of these fractions to reduce them into the smallest set of integers.

−1,0,2

Therefore, the miller indices for the given plane is 1,0,2.

Important Features of Miller Indices

Some important features of Miller indices have been mentioned below as:

1. A plane that is parallel to in the least one of the coordinate axes comes with an intercept of infinity ([infty]) and consequently, the Miller index for the said axis becomes zero.

2. All of the similarly spaced parallel planes having a specific alignment come with the same index number (h k I).

3. Miller indices don’t only give the definition of the specific plane but a combination of many parallel planes.

4. Only the ratio of indices is considered important over everything else. The planes do not matter.

5. A plane fleeting over the origin is defined in comparison to a parallel plane that has non­zero intercepts.

6. Altogether the parallel equally far planes consist of the same Miller indices. Therefore, the Miller indices are used in relation to a set of parallel planes.

7. A plane that is parallel to anyone out of the many coordinate axes comes with an intercept of infinity.

8. If the Miller indices relating to two planes comes with the same ratio, for example, 844 and 422 or 211, then the planes can be proved as parallel to each other.

9. If h k I am the Miller indices relating to a plane, then the plane will divide or cut the axes into a/h, b/k, and c/l equivalent sections individually.

10. If the integers that are being used in the Miller indices comprise more than one single digit, the indices must be parted by commas for precision, for example (3, 11, 12).

11. In a family the crystal directions are not necessary to be parallel to each other. Likewise, not all members in a family of planes are supposed to be parallel to each other.

12. By altering the signs of entirely each one of the indices of a crystal direction, we find the antiparallel or conflicting direction. By altering the signs of each and every one of the indices of a plane, we get a plane that is situated at a similar distance on the other side of its origin.

After the experimental confirmation of Rutherford’s scattering theory in about the year 1913, the one-to-one relationship or link of an atom with its atomic number Z was proven by the work of Henry Moseley from the year 1887 to 1915. 

Henry Moseley used the structure of Bohr’s atomic model to determine the energy radiated by an electron when it migrates from low-level orbitals. This energy released during migration has a strong dependence on an atomic number ‘Z’ so that by measuring the energy of the X-rays characteristic of any element, its atomic number Z can be confidently determined. 

Moseley Periodic Law

Here, we will measure the x-ray spectra of a number of elements and also identify several unknown elements by looking at their characteristics, viz: X-ray spectra.

Moseley’s law was discovered and published by an English Physicist named Henry Moseley. This law is an empirical law that concerns the characteristics of X-rays emitted by atoms.

The frequency v of X-ray emitted by an atom is related to its atomic number ‘Z’ by the following formula:

v =(a−b)−−−−−− [sqrt{(a-b)}]        …..(1)

Here,

a and b = are constants. We also call these constants proportionality and screening or shielding constants.

Equation (1) is Moseley’s X-ray Characteristic formula and here the two physical constants ‘a’ and ‘b’ are independent constants of an element; however, these two depend on the X-ray series.

For a ‘k’ series, the value of a and b is:

a = [frac{3RC}{4}]−−−−−−[sqrt{frac{3RC}{4}}]

and

b = 1 

Where,

R = Rydberg’s constant

c = speed of light

For the L series, the value of a and b is as follows:

a = [frac{5RC}{36}]———– [sqrt{frac{5RC}{36}}],

and

b  = 7.4

The relation between a and b is determined by experiments using Henry Moseley’s law and the graph for this relationship is as follows:

The line intersecting in the graph at the Z-axis shows that Z = b, where b is 1 for K series elements and 7.4 for elements in L series.

Moseley Law Statement

A simple idea is that the effective charge of the nucleus decreases by 1 when it is being screened by an unpaired electron that persists behind in the K-shell.

Moseley X-Ray Experiment

X-ray spectrometers are the fundamental foundation-stones of the process of X-ray crystallography. 

The working by Moseley by employing X-ray spectrometers is as follows:

A glass-bulb electron tube was used, inside this evacuated tube, electrons were fired at a metallic substance, which was a sample of the pure element in his work.

The firing of electrons on a metallic substance caused the ionization of electrons from the inner electron shells of the element. The rebound of electrons into the holes in the inner shells then caused the emission of X-ray photons leaving out the tube in a semi-beam, through an opening in the external X-ray shielding. 

Now, these radiated X-rays were then diffracted by a standardized salt crystal, with angular results emitting in the form of photographic lines by the exposure of an X-ray film fixed at the outside the vacuum tube at a known distance. 

Next, Moseley employed the application of Bragg’s law after initial guesswork of the mean distances between atoms in the metallic crystal, based on its density next leading to calculate the wavelength of the emitted X-rays.

Analysis of Moseley’s Experiment

To Determine the following things:

• Firstly, we must confirm Moseley’s law with six known samples of elements. Since the energy is the characteristic X-ray (according to Moseley), which is proportional to (Z – n and channel number N is directly proportional to E, then N is proportional to (Z – n). Therefore, N kZ = − bg n. 

• Draw a graph plotting N vs. Z for the six known samples. Obtaining the best values of k and n can be observed from this graph. Now, look at your spectra carefully and think about what the uncertainties in your data are. Devise a reasonable method for determining the uncertainties in n and k.

• Determine Z for the unknowns by comparing the peak position for each with your results from the six known samples and also determine the uncertainty associated with your findings.

So, this is how we can determine the atomic number of a material; by observing the X-ray characteristic of an element. 

Moseley’s Law and a Basic Introduction

Moseley’s law is used to understand the emitted x-rays by the atoms. This law was derived and published by Henry Moseley. He used this law to determine the energy exerted by an atom. Atoms are the smallest particle that exists. And to find the energy that is exerted by the atom, Moseley’s law is used. It is an empirical law that determines the atomic number. 

Students can find more information about Moseley’s law on the website. It has all free downloadable content that students can use and study. It is important to practice all the formulas with example questions to get a better understanding of the law. This law is very important as it created the basis of the periodic table and also helped in discovering new elements that were previously unknown to the scientists. 

Statement of the Moseley’s Law

The statement of moseley’s law is: “The square root of the frequency of the x-ray emitted by an atom is proportional to its atomic number”. New elements were also found because of this law. This law came to existence because when Henry Moseley was studying graphs, he found a strange relationship between the lines and the atomic number. This law also helped with organizing the elements on the periodic table based on atomic numbers rather than atomic mass. 

The formula for Moseley’s law is ν=a(Z–b)…(1) 

Importance of Moseley’s law 

Moseley’s law is very important because it proved that atomic numbers are more necessary than atomic mass and it is because of this reason that the entire periodic table was changed based on the element’s atomic number. This law also helped with discovering new elements and explained the property of elements way better. 

In 1914, Moseley also published a paper where he spoke about three unknown elements between two others and because of all his experiments and data, we now have more information about how to study elements. He also found that the K lines were related to the atomic number and later found the formula by which the approximated relationship between them could be calculated. 

The formula which is called Moseley’s Law is: 

V = A . (Z – b)²

In this case,