Category: Physics Notes PPT

Do you know what is a photon? Well!! Light emits a packet of energy, these chunks are photons and each photon carries its own energy, which is the photon energy.

The formula of energy of photon helps calculate the energy carried by each photon, which is given as:

                            E   =  hf….(1)

This energy of photon equation is also known as Planck-Einstein Relation.

Here,

E is the photon energy, i.e., the energy of a photon equation for a single photon

h  =  it is a constant, known as Planck’s constant.

f  =  the electromagnetic frequency, measured in Hertz or Hz

The above energy of a photon equation is valid for a single photon, if there are ‘n’ no of photons emitted by your tube light, then the no of photons formula is:

                      E  =  n* h* f

So, putting n = 1, we get the energy of one photon formula.

Here, energy ‘E’ is calculated in both J and eV, depending on the system of unit used. 

On this page, we will understand the formula of photon energy, no of photons formula, photon wavelength formula, and the kinetic energy of photon formula.

Photon Energy

We can express the photon energy by using any of the units of energy. 

Among the units, we commonly use the electronvolt (eV) unit of the photon energy and the joule (it’s multiple, such as microjoule). 

As 1 Joule =  6.24 × 10[^{18}] eV, however, the large units are often useful in denoting the photon energy with higher frequency and higher energy, such as gamma rays, as opposed to lower energy photons, like those in the radiofrequency region of the electromagnetic spectrum.

Now, let’s understand the photon energy formula in more detail:

Formula of Photon Energy

The photon energy formula can be rewritten in the following way:

                         E  =  hf  

Also, the energy photon formula frequency is c/λ. Putting the value of ‘f’ in the above equation:

                              E =  hc/λ      ….(2) 

E is the photon energy in Joules

λ is the photon’s wavelength in metres

c is the speed of light in a vacuum, whose value is 3 x 10[^{8}] metres per second

h is the Planck constant –  Its value is 6.626 × 10[^{-34}] kgm[^{2}]s[^{-1}] or J.s

The photon energy at 1 Hz is equal to 6.626 × 10[^{-34}] J

Planck’s constant can be written in terms of eV, which is 4.14 × 10[^{-15}] eV· s.

Energy of Photon Formula

From the energy of photon equation, we see that the energy of photon depends on the following parameters:

• The energy of photon is directly related to the photon’s electromagnetic frequency.

• The energy of photon depends on wavelength in such a way that the energy of photon is inversely proportional to the wavelength. 

• The higher is the photon energy frequency, the higher its energy. In contrast, the longer is the photon’s wavelength, the lower its energy.

Photon Wavelength Formula

We know that a photon is characterized by either a wavelength ‘λ’ or equivalently energy, ‘E’. 

Also, there is an inverse relationship between E and λ, as stated in equation (2).

On multiplying the values of h and c as;

 h * c  =  (6.626 × 10[^{-34}]J.s) * (2.998 × 10[^{8}])  =  1.99 × 10[^{-25}] J.m

The above inverse relationship helps us understand that the light of high-energy photons (such as “blue” light) has a short wavelength whereas the light of low-energy photons (such as “red” light) has a long wavelength.

While dealing with “particles” like photons, eV or the electronvolt is the most commonly used unit of energy than the joule (J). An electron volt is the energy needed to raise an electron through 1 volt, thus the photon energy in 1 eV = 1.602 × 10[^{-19}] J.

Therefore, the expression of hc in terms of eV will be:

hc = (1.99 × 10[^{-25}] J-m) × (1ev/1.602 × 10[^{-19}] J) = 1.24 × 10[^{-6}] eV-m

Further, writing the units for λ in terms of µm:

hc = (1.24 × 10[^{-6}] eV-m) × (10[^{6}] µm/ m) = 1.24 eV-µm

By expressing the energy of a photon equation in terms of eV and µm we arrive at a commonly used expression that relates the photon’s energy and wavelength, which we will understand under the further “energy of photon formula in eV” section.

Energy of Photon Formula in eV

Energy is often measured in electronvolts.

The photon energy formula in electronvolts can be written by using the wavelength in micrometres, which is as follows:

                             E (eV)   = [frac{1.2398}{lambda (mu m)}]…..(3)

This equation is also known as the photon wavelength formula.

From equation (3), we observe that the exact value of 1 × 10[^{6}] (hc/q) is 1.24 but the approximation of 1.24 is sufficient for most purposes.

Also, this equation is significant for the wavelength in micrometres. From the above energy of photon formula in eV, we infer that photon energy at 1 μm wavelength, the wavelength of near-infrared radiation, is approximately 1.2398 eV or 1.24 eV.

Kinetic Energy of Photon Formula

Since we know that the electrons are tightly bonded to the metal, so we need the energy to help them come out of the metal, i.e., to lead the photoemission process. So, the electrons that come out of the metal have some energy. 

Therefore, the maximum kinetic energy of ejected electrons is shown below: 

                                          KE[_{e}]   =   hf – BE….(4)

Here,

E is the photon energy

BE = binding energy or the Work function of the electron, which is particular to the given material.

KE[_{e}] = kinetic energy (in Joules)

Kinetic Energy vs Frequency Graph

The graph for the above equation is shown below:

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The above graph is between the kinetic energy of an ejected electron, KE[_{e}], and the frequency of electromagnetic radiation influencing a certain material. 

There is a threshold or a limited frequency below which no electrons can eject because each photon interacting with its respective electron has insufficient energy to break it away or leave its lattice point. 

Above all, the threshold energy, KE[_{e}] increases linearly with the frequency ‘f’, which remains consistent with the relation in equation (4). 

Besides this, the slope of this line is ‘h.’ So, this data can be utilized to ascertain Planck’s constant experimentally. 

Do you know that Einstein gave the first-ever successful explanation of the above data by proposing the notion of p
hotons-quanta of EM radiation?

Photon Applications 

• An FM radio station transmitting 100 MHz electromagnetic frequency releases photons with an energy of around 4.1357 × 10[^{-7}] eV. From the mass-energy equivalence), we understand that this amount of energy is approximately 8 × 10[^{-13}] times the electron’s mass, i.e.,  9.1 x 10[^{-31}] kg.

• Gamma rays are considered of very high energy, They have photon energies of 100 GeV to over 1 PeV, i.e., from 10[^{11}] to 10[^{15}] eV, or 16 nanojoules to 160 microjoules. This relates to frequencies of 2.42 × 10[^{25}] to 2.42 × 10[^{29}] Hz.  

Conclusion

So, we have the following two formulas for the energy of photon calculator:

We use the term ‘force’ in our daily lives to refer to a number of things. In most contexts, force is used to describe any push or pull that requires an effort at a certain speed, in some cases. When objects interact with each other, it is possible that they exert a certain amount of force on each other as well. 

What Is the Average Force?

Average force is the force applied to a body that is moving at a certain velocity, for a certain period of time. This is almost always a vector quantity, which means that it has both magnitude as well as direction. It is called average force to imply that it is not a constant or absolutely measured value for velocity. 

Formula For Average Force

If the time interval is taken as t, the force will then be the frequency of the change of momentum. When there are a number of time intervals, the rate of change of  momentum is known as the average force. 

Therefore, it is shown as:

[F = frac{m (v_f – v_i)}{Delta t}]

Here, 

m refers to the mass of the body

vf is the final momentum

vi indicates to the initial momentum 

Δ t points to the change in time, or time intervals

The product of the average force is always expressed in the form of Newtons (N). 

Formula For The Magnitude Of Force

Magnitude of force formula: F = m*a

Here,

m refers to the mass

a refers to the acceleration

What Is Net Force?

There is a certain net force that acts upon all objects.  This is the vector sum total of all forces that are acting on any particular object. Newton’s second law indicates that if there is a net force acting on any particular object, that object is accelerating, so its speed will change with every second. 

Solved Examples Using Average Force Formula

Example1:

A man throws an object with a mass of 7 kg and it rolls with a velocity of 4 m/s for 2 s. Find out its average force.

Solution:

Given: Mass of bowling ball m = 7 kg,

Initial velocity vi = 0

Final velocity vf = 4 m/s

Plugging in the values in the Average force formula, we have:

[F = frac{m (v_f – v_i)}{Delta t}]

[F = frac{7 (4 – 0)}{2}]

F= 14 N

Example 2:

A rabbit that weighs 20 kg chases the owner for 16 seconds with a velocity of 7 m per sec. Calculate the average force for the rabbit.

Solution:

Given:

The mass’ m = 20 kg.

The rabbit’s average velocity, Vavg = 7 m per s

The time, Δt =16seconds.

Now, the formula is,

[F = frac{m (v_f – v_i)}{Delta t}]

[F = frac{20 (7 – 0)}{16}]

[F = frac{140 text{kg m per s}}{16sec} ]

= 8.75 kg m per s²

Hence, the average force is  8.75N.

Conclusion

Average force can be defined as the force applied to a body moving at a certain velocity, for a certain period of time. It is mostly a vector quantity since it has both momentum and direction. It is different from net force and momentum. 

Physics is all about learning the mechanics of life. Work, energy, and power are the most important physical aspects that are widely used in the physical world. Physics involves many interesting concepts such as kinematics, one-dimensional motion, and many more and these are categorised under classical physics. Just like classical physics, there are various branches of physics depending upon the subject of discussion. Electrodynamics or electrical circuit theory is the study of electrical connections used in the day to day activities. Electric power is the most commonly used term in circuit theory. 

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The electric power formula deals with the rate of work. We know that power is the rate of doing work, similarly electric power is a very important thing that enables us to observe the rate at which electrical energy transfers from an electric circuit, i.e., rate of transfer of electrical energy. In this article, we will learn about the electric power formula, electrical energy formula, and the formula of power consumption with solved numerical.

Electrical Energy Formula

The electrical power formula is analogous to the mechanical power formula, we notice that electric power is the rate at which work is being done or in other words, electrical power is the rate at which electrical energy is transferred. The electrical power is measured in watts. Now, electrical energy is the energy derived from electric potential energy or kinetic energy of the charged particles. Electrical energy is a very important concept in physics, yet it is frequently misunderstood because of its definition. Then what exactly is electrical energy, what is the electrical energy formula and what are important steps and the rules that will be applied when it is used in calculations? 

Let us have a look at the electrical energy formula. We know that an electrolytic battery will have two terminals, one is positive and the other is negative, familiarly known as the anode and cathode of the battery. The potential difference developed between the two terminals is known as the voltage or emf.  Mathematically, let us assume that the two terminals of the battery are A and B, let V₁ and V₂ be the potentials at terminal A and B respectively. 

The potential difference (or the voltage) across terminal A and B is given by the following equation:

⇒ V = V₁–V₂ = -(V₂–V₁)…….(1)

and this must be a positive quantity i.e., must be greater than zero.

Now, we know that electric current is the flow of electrons or in other words flow of electrical charges, then we can define electrical current as the rate of conduction of electrical charges or the rate of flow of electrical charges in a given cross-sectional area. The kinetic energy of these charges will be conserved and hence the total electrical energy will be stored in the form of potential energy. Then the potential energy of the charge Q at terminal A will be equal to QV₁, similarly, the potential energy of the charge Q at terminal B will be Q V₂. Thus the total change in potential energy of the system is given by:

⇒ΔU=final potential energy – initial potential energy

⇒ΔU=ΔQ (V₂–V₁)

⇒ΔU = -I Δt V ( because I = [frac{ΔQ}{Δt}])…….(2)

If we consider the total kinetic energy of the system into account, it would also change if the charges inside the conductor moved without collision. This is to maintain the total energy of the system unchanged. Thus, according to the law of conservation of total energy, we have:

⇒ Kinetic Energy = U

Or

⇒ Kinetic Energy = -I V Δt >0

Thus, in the external or internal electric field, if the charges move freely across the conductor, there would be a gradual increase in the kinetic energy as they move without any constraints.

When the charges undergo collision, the total energy gained by them is shared between the atoms. Consequently, the vibration of the atoms within the conductor will be increasing which in turn result in the heating up of the conductor. Thus, some amount of the total energy is dissipated in the form of heat in an actual conductor.

The electrical energy is measured in terms of the joule or watt-second. Electrical energy is said to be of one joule when one ampere of current flows through the given electrical circuit for a second when the potential difference of one volt is applied across it. 

The kilowatt-hour (kWh) is the commercial unit of electrical energy, which is also known as the Board of Trade unit (B.O.T). And usually, one kwh is called one unit.

1 kwh = 1000 x 60 x  60  watt – second

1 kwh = 36 x  10⁵ Ws or Joules

This equation is known as the electrical energy unit conversion formula or electrical unit calculation formula.

Formula of Power Consumption

We know that, according to the definition of the electrical power formula, it is the rate of transfer of electrical energy by an electrical circuit per unit of time. Here the total electrical energy can be either kinetic energy or potential energy. In most cases, only potential energy is considered, which is the energy stored in the system due to the relative positions of charged particles or electric fields. Now, how do we calculate the electric power? What is the formula of power consumption to be followed while solving the problems? 

The electrical power formula is given by:

⇒ P= VI

The electrical power formula is written by using ohms formulas and it is also known as the power voltage current formula and  is given by:

⇒ P = I²R=[frac{V^{2}}{R}]

Now,  we should note that an electrical circuit element having a power profile that is both positive and negative over some period of time interval could consume or produce energy according to the sign of the integral of power. If the power is constant over the time interval then the energy or the formula of power consumption can be expressed simply as:

⇒ E = P t

 

The above expression is known as the formula of power consumption or electrical power equation.

Example

1. If the Current and Voltage of an Electric Circuit are Given as? 3 Amp and 10 Volts Respectively. Calculate the Electrical Power of the Circuit?

Solution:

Given,

The total current flowing in the circuit = I =3 amp

The potential difference measured across the circuit=V=10 volts

We are asked to determine the electric power, we know that the electric power formula is given by ohms formulas:

⇒ P = V x I

Where,

V-The applied voltage

I-The current flowing in the circuit

Substituting the required data or values in the above equation, we get:

⇒P =10 x 3 = 30 watts

Therefore, the total electrical power of the circuit is 30 watts.

(Image to be added soon)

The mirrors which we use in the cars to see the back side are known as the spherical mirrors. The mirrors which are the spherical one, are the mirrors having curved surfaces that are painted on one of their sides. The spherical mirror is a mirror in which inward surfaces are painted and are called convex mirrors while the mirrors in which outward surfaces are painted are called concave mirrors. In this article we are going to discover more about the topic.

Surface Area of a Cylinder

A cylinder generally is a three-dimensional structure having circular bases parallel to each other. Generally we see that the area of the three-dimensional shapes refers to the surface area. The surface area that is represented is in the units of square. For example we can say that cm², m², and so on etc. A cylinder which we are talking here can be seen as a set of circular disks that are stacked on one another.  Since we see that the cylinder is a solid of a shape which is three-dimensional  it has both volume and surface area. 

The area of the cylinder is defined as the sum of the curved surface and the area of two circular bases of the cylinder.

The area of the cylinder is said to be the total region which is covered by a cylinder in three-dimensional space. The area of a cylinder is said to be equal to the sum of the area of two circular bases and curved in area of surface. In right cylinders the two bases which are circular are exactly over each other and the axis line produces a right angle to the base. In case if one of the bases which is circular  is displaced and the axis does not produce the right angle to the base then it is known as the oblique cylinder.

In the middle of the two bases of  circular, there is a surface which is curved which when opened generally represents a rectangular shape. This is a curved surface and is also known as the lateral surface. The different parameters that are used to calculate the area of the cylinder include height and radius, axis, base, and side. The radius which is of the cylinder is generally defined as the radius of the circular base.

Surface Area of a Sphere

 A Sphere that is a three-dimensional solid is having a round shape that is just like a circle. The formula which is of total surface area of a sphere that too in terms of pi denoted by π is given by:

The surface area is given as =  4 π r2 square units

The difference between a sphere and a circle is that a circle is a figure which is two-dimensional or we can say that a flat shape whereas a sphere is a shape which is three-dimensional. Therefore we can say that the area of the circle is different from the area of the sphere. 

Area of circle is denoted as = π r2 

From a perspective which is visual, a sphere has a three-dimensional structure that forms by rotating a disc that is circular with one of the diagonals.

Let us consider that an instance where spherical ball faces are painted. To paint the whole surface we can see that the paint quantity required has to be known beforehand. Hence the area which is of every face has to be known to calculate the quantity of the paint for painting the same. We can generally define this term as the total surface area.

The surface area that is of a sphere is equal to the area of the entire face surrounding it.

Surface Area of a Cone

The Cone is said to be a structure which is three-dimensional which has a circular base where a set of line segments connect all of the points on the base to a common point called apex. A cone can be seen as a set of circular non-congruent discs that are stacked on one another in such a manner that the ratio of the radius of adjacent discs remains constant. We can think of a cone as a triangle which is being rotated about one of its own vertices. That is the curved surface area of a cone = πrl

And the total surface area of a cone = πr(l+r)

The curved surface which is of a cone is the area of the cone that is excluding the base. In other words we can say that it is the area of the cone when it is unfolded. The formula which is to calculate the curved surface area that too of a cone is given by:

The curved Surface Area that is the CSA = πrl

Here we can see that:

Letter r = is the radius of the circular base of the cone

Letter l = is the slant height of the cone

Black holes are among the most mysterious and fascinating objects or the celestial things investigated by modern scientists and astrophysicists. The concepts of the black holes on investigation helped us to illustrate the effects of the theory of relativity in a most spectacular way. The strong curvature of space-time around them prevents not only all their light from reaching us, but has an equally striking effect on time. The study of black holes reveals many interesting and mysterious things regarding the universe. 

As the advancements took in the study of the black holes, now a new visualization and observation of a black hole illustrate how its gravity distorts our view (it is assumed that nearby black hole the gravitational pull will be extremely high), wrapping its surrounding regions as if seen in a carnival mirror. The visualization simulates the appearance of a black hole where the infalling matter has collected into a thin, hot structure known as an accretion disk. 

Accretion Disc

The black hole’s extreme gravity skews all the photons emitted by different regions of the disk, producing the misshapen appearance. Due to the extreme gravitational force, the black hole attracts all the materials, such as the dust, gas, and other stellar debris that has arrived closer to the regions of the black hole but not yet got into the black hole will form a flattened spinning band of the material or the matter around the event horizon, is called an accretion disk.

An accretion disc is a crucial tool for the investigation of black holes. Almost everything we know about black holes and has learned about black holes is with the help of the study of accretion disc or accretion disks. Why the accretion disks are of this important? One of the most important thing that had changed the view of astronomy from the ground was when the scientists realized that there was more to see and analyze about the universe than what optical telescopes had until then allowed them to observe. 

After a period of time astrophysicists have discovered that visible light was only a small fraction of the whole electromagnetic spectrum and that information travel through the universe on various wavelengths from short-range to long-range, i.e., from radio, through microwave, infrared, optical, ultraviolet, X-ray, to gamma rays. Since then, everything we learned and witnessed about the universe is with the aid of electromagnetic radiations and many mysterious aspects of the universe have learned from electromagnetic radiation. 

As a matter of fact and study, the black holes do not emit any kind of radiation and that would make them impossible to study if they did not have accretion discs around them. Those black hole accretion disks are what we actually study, observe, and from what we collect and synthesize properties of their central gravitating objects.

Black Hole Accretion Disk

A black hole is a region where the gravity is found to be so strong that any light or the photons that try to escape gets dragged back. Because nothing can travel faster than light, everything else will definitely get dragged back too, if it is too near the region of the black hole. So, if any matter falls into the black hole, it would never get out of it. A black hole has always been thought of as the ultimate prison from which there is no escape!! 

Let us understand, what a black hole is made of or what it consists of. According to the study of the black holes till today, it is found that it is an edge and it is called a horizon. We can say this horizon is analogous to the edge of a waterfall. A black hole is also appeared to have a thin band around it made of all the stellar debris, dust and matter that was passing through the event horizon and this band of matter which is at the edge of the horizon and has not fallen into the black hole is known as an accretion disk.

What do we mean by the black hole accretion disk? Basically, an accretion is nothing but just a process of growth of a massive object by gravitationally attracting (using extreme gravitational forces) and collecting all the additional material or matter. Typically, this ends up forming a disk-like structure of diffused matter or the material or gas that is in orbital motion around the central accreting object. Accretion disks are the most important features in the universe and can be found even around smaller stars or stellar remnants, in close binary stars, in the centres of spiral galaxies, in quasars, and also they can be formed in gamma-ray bursts.

The accretion disk can have many forms. It can be either spherical or planar. It can also be either persistent or episodic. The usual observation for accretion is that the material flows from one celestial object to another. Then there exists a preferred direction given by the particular orbital plane of the two bodies. The flow of the matter also keeps that plane but does not extend straight from one object to the other since it has some angular momentum generated from the orbital motion of the two. It is pushed a little bit aside by Coriolis force and forms a disk around the target object and that disk is named an accretion disk.

In an identical way, the matter piles up in a dense spinning accretion disk orbiting a black hole, star or other gravitating objects. Friction between adjoining layers will cause the gas in the disk to heat up as its potential energy will slowly dissipate into heat. The gas also loses its angular momentum which allows it to get closer to the central object and orbit faster than desired time. But, the faster motion will result in more friction and as the gas gets very hot it radiates out energy (usually in the form of light). Ultimately, It depends on the mass of the central object what temperature the disk can reach, the more massive it is the lower temperature the disk has. 

Luminous Black Hole Disks

The most effective collectors of matter are the most compact objects present in the cosmos, and they are definitely the black holes. The black holes are the perfect spacetime traps, it means that nothing that falls into a black hole can ever escape from it, not even light!! Therefore, black holes are indeed as black as their name indicates (i.e., the complete absence of light), and the study of black holes are very difficult for astronomers to detect. At the same time, one of the fascinating pieces of information about the black holes is, the entire situation will change dramatically once a black hole is fed with enough matter from its vicinity, then, black holes can transform their surroundings into the brightest and most spectacular regions of the cosmos!!! 

There are several different ways for black holes to light up their entire cosmic neighbourhood. Some require very special and controlled circumstances, but one is universal, wherever matter falls into a black hole, then it will result in the production of thermal radiation (emitting light radiation). Matter falling towards a central object under the influence of high gravity gets accelerated to higher and higher speeds, gaining more and more kinetic energy. But once a particle of infalling matter is attracted to an accretion disk and then the particle’s motion will be disturbed. 

Due to frequent collisions between all the different particles of the stellar matter, there are no well-defined simple orbits. Instead, the whole ensemble of particles is in random motion. Such random motion with eddies and instabilities is just like in a turbulent fluid and is commonplace within accretion disks. We know that according to the definition, disordered microscopic particle motion
is thermal motion, and as such directly related to temperature. As the motion of the infalling particles becomes more random or chaotic, matter in the accretion disk is heated to very high temperatures, which further end up emitting the photon radiations. 

The accretion disks around stellar-mass black holes i.e., black hole accretion disks have temperatures around millions of Kelvins and radiate in the form of X-rays, at the same time the accretion disks around supermassive black holes have temperatures around thousands of Kelvins and radiate in optical or ultraviolet light.

The study of black holes is not as easy as the theory suggests, it is so hard to detect a black hole and in fact, till the date, no astronomer has managed to take detailed images of the accretion flow onto a central black hole, that might require a higher resolution than current advanced telescopes can provide.

Nowadays the astrophysicists have indirect ways of testing their assumptions about what happens to the matter that is near the regions of the black holes. Using advanced technologies, such as using computer simulations, astrophysicists can predict the spectra of accretion disks, i.e., accretion disk emits electromagnetic spectrum and the way the radiation energy is distributed among the different frequencies can be studied. 

The spectra emitted by the accretion disks carry a clear imprint of the local conditions, such as a strong gravitational redshift tells of the central object’s compactness, and a systematic Doppler shifts record how matter transit at nearly the speed of light (to be noted not equal to the speed of light) in the surrounding of an accretion disk. Whenever observations show the mass concentrated in the innermost region to be high enough, where there is a complete absence of light or with no luminous object visible at that particular spot, at such locations, there is a strong likelihood for the central object to be a black hole.

From this list of salient features and the characteristic properties of black holes, astronomers have a clear notion of what to look for, and, as it turns out, there are indeed objects in the night sky with exactly the required properties. In fact, for a number of required objects, the match between prediction and observation is quite impressive, many space stations are working on this rigorously. Thus, it appears that our universe does actually contain the required amount of black holes accreting matter. 

Also due to the presence of high gravity around a black hole, an object in its gravitational field experiences a slowing down of time, known as gravitational time dilation, relative to observers outside the field. From the viewpoint of a distant observer, an object falling into a black hole appears to slow down and fade away after some time, eventually, it is all based on the theories that have been studied and till date, the observations are going on to understand the process of black holes. And the particles that are attracted to the black hole disk or black hole accretion disk will appear to be approaching but never quite reaching the event horizon. Ultimately, at a particular point of time just before it reaches the event horizon, it becomes so dim that it can no longer be seen (due to the time dilation effect).

The accretion disks have been a gift for many astronomers, as a recent advancement in the study of the black holes is identified with the help of the accretion disk that gave evidential information regarding the presence of gravitational waves.

Did You Know

• There is a huge misconception about black holes, many think that the black holes are like cosmic vacuums that suck everything around their neighbourhood in space, but in fact, black holes are like all other objects in space, albeit with a really strong gravitational field.  For example, if you replace the Sun with a black hole of equal mass, Earth would not get sucked in, it would rather continue orbiting the black hole as it orbits the Sun, today. 

• Black holes appear like they’re sucking in matter from their surrounding, but that’s a common misconception. The fact is that many companion stars shed some of their mass in the form of stellar wind, and the matter in that wind then falls into the grip of its hungry neighbour, a black hole.

• Though the blackholes will not suck the entire matter present around them, one of the most interesting aspects of the black holes is that they have this incredible ability to literally stretch everything into a long spaghetti-like strand. Appropriately, this phenomenon is known as spaghettification!!

Alpha decay or α-decay refers to any decay where the atomic nucleus of a particular element releases 42He and transforms into an atom of a completely different element. This decay leads to a decrease in the mass number and atomic number, due to the release of a helium atom.

To understand this entirely, consider this alpha decay example. Suppose element Z has mass number ‘a’ and atomic number ‘b’. During α decay, this element changes to X. Take a look at the equation below. 

abZ → a-4b-2X + 42He

Thus, you can see that the mass number and the atomic number balances out on both sides of this equation.

Alpha Decay Example Problems

Now, using the same concept, solve the following problem. A Uranium nucleus, 23892U undergoes alpha decay and turns into a Thorium (Th) nucleus. What would be the mass and atomic number for this resulting nucleus after the decay?

Solution – 

23892U → 238-492-2Th + 42He → 23490Th + 42He

Therefore, the resulting Thorium nucleus should have 234 mass numbers and 90 atomic numbers.

Alpha Decay Equation

Alpha decay formula can be written in the following way – 

AZX → A-4Z-2Y + 42α

In this equation, AZX represents the decaying nucleus, while A-4Z-2Y is the transformed nucleus and 42α is the alpha particle emitted.

Understanding Q Value of Alpha Decay

In Physics and Chemistry, Q-value is defined as the difference between the sum of the rest masses of original reactants and the sum of final product masses. In simpler terms, you can say that the Q-value is the difference between the final and initial mass energy of the decayed products.

For alpha decay equations, this Q-value is,

Q = (mX – mY – mHe) c2 

The energy Q derived from this decay is divided equally into the transformed nucleus and the Helium nucleus.   

Gamow Theory of Alpha Decay

Gamow’s Theory of Geiger-Nutall law defines the relationship between the energy of an alpha particle emitted with the decay constant for a radioactive isotope. It was derived by John Mitchell Nutall and Hans Geiger in 1911, hence the name for this law. 

With this rule, it becomes abundantly clear that shorter-lived isotopes emit greater energy when compared to isotopes with longer lives. However, α decay is just one type of radioactive decay. A nucleus can undergo beta and gamma decay as well.

What is Beta Decay?

In beta decay, the radioactive isotope emits an electron or positron. This decay occurs by following the radioactive laws, just as alpha decay does. An example of beta decay is – 

3215P → 3216S + e– + v– 

What is Gamma Decay?

The last form of radioactive decay is gamma decay. Here, a high-energy radioactive nucleus can lower its energy state by emitting electromagnetic radiation. Gamma decay is common for the daughter nucleus formed after α decays and ß decays. 

This happens because daughter nuclei in both these forms of decay are in a heightened state of energy. To return to a stable state, these nuclei emit electromagnetic radiation in the form of one or multiple gamma rays. 

What are the Major Components of the Equation that Represents Alpha Decay?

The general equation of alpha decay contains five major components like the parent nucleus which is the starting nucleus, the total number of nucleons present in the nucleus (that is, the total number of neutrons and protons present in the nucleus), the total number of protons in an atom, the daughter nucleus which is the ending nucleus and the alpha particle that is released during the process of alpha decay.

What is the Safety Level of Alpha Decay?

Though the alpha particles are not very penetrating, the substance that undergoes alpha decay when ingested can be harmful as the ejected alpha particles can damage the internal tissues very easily even if they have a short-range. This is basically due to the contact of emitted particles with membranes and living cells. 

The major health effects of alpha particles depend on the time and reason due to exposure to alpha particles. If in case the alpha particles are swallowed, inhaled, or absorbed into the bloodstream which can have long-lasting damage on biological samples. The damage caused due to alpha particles increases a persons’ risk of cancer like lung cancer. Radon which is an alpha emitter, when inhaled by individuals can cause related illnesses in humans.

Exercise

14964Gd undergoes α decay to form one nucleus of Sm. Calculate the atomic and mass number of the daughter nucleus.

Solution – 

14964Gd → 149-464-2Sm + 42He → 14562Sm + 42He

As per the alpha decay equation, the resulting Samarium nucleus will have a mass number of 145 and an atomic number of 62.        

 

The isotope element that emits radiation is known as the Radioactive Element. This element is also the object that undergoes radioactivity. 

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