Photoelectric Effect MCQ for IOE and Class 11,12.

 Photoelectric Effect MCQ for IOE and Class 12.

 Quantum Nature of Radiation

The quantum theory of radiation was first proposed by Planck in 1901 to explain the black body radiation. According to this theory, these radiation from the body is emitted in separate packets of energy each packet is called a quantum of energy. Each quantum carries a definite amount of energy called photon, given by

            E= hf    .......1

where f is the frequency of radiation and h is a constant called the Planck constant whose value is 6.62 x 10^-34 joule sec.

This is the quantum theory of radiation. From Eq. (1) the photons or quanta with high frequency have a large amount of energy while those of low frequency have less amount of energy.

 Einstein's Photoelectric Equation; Stopping Potential

Whenever light or electromagnetic radiation such as X-rays, ultraviolet rays fall on a metal surface, some electrons are emitted from the surface. This phenomenon of emission of electron from a metallic surface when radiation of suitable frequency falls on it is called photoelectric effect. These electrons are called photoelectrons.

Metals like Zinc, Cadmium, etc. are more sensitive only to ultraviolet light where as alkali metals like Sodium, Potassium etc. are sensitive even to visible light.

Laws of Photoelectric Emission

1. For every metal, there is a particular minimum frequency of the incident light, below which there is no photoelectric emission, whatever be the intensity of the radiation. This minimum frequency, which can cause photoelectric emission, is called the threshold frequency.

2. The rate of emission of electron is directly proportional to the intensity of the incident light, provided the frequency is greater than the threshold frequency.

3. The velocity and hence the energy of the emitted photoelectrons is independent of the intensity of the light and depends only in the frequency of the incident light and the nature of the metal.

4. There is an instantaneous emission of photo-electrons within the limits of experimental accuracy.

5. The maximum velocity V_max. and hence the stopping potential Vo are independent of the intensity of the incident light radiation but are directly proportional to the frequency of the incident radiation for a given metal.

The photoelectric effect is a phenomenon in which electrons are emitted from a material when it is exposed to electromagnetic radiation, such as light. Some key points to keep in mind when considering the photoelectric effect include:

• The energy of the photons (i.e. the particles of light) must be greater than the work function of the material in order to cause the emission of electrons. The work function is the minimum amount of energy required to remove an electron from the material.
• The number of electrons emitted is directly proportional to the intensity of the incident radiation. However, the kinetic energy of the emitted electrons is dependent on the frequency (and therefore energy) of the photons.
• The photoelectric effect cannot be explained by classical wave theory, but requires a quantum mechanical explanation.
• Einstein proposed that the energy of a photon is directly proportional to its frequency (E = hf), which helps to explain the dependence of the kinetic energy of the emitted electrons on the frequency of the incident radiation.
• The photoelectric effect has numerous applications in fields such as solar energy, electronics, and quantum mechanics.

When approaching MCQs related to the photoelectric effect, it is important to keep these key points in mind and to carefully consider the information provided in the question and answer choices.

Some Questions Related to Photoelectric Effect 

1. What is the work function of a material and how does it relate to the photoelectric effect?

👉The work function is the minimum amount of energy required to remove an electron from a material. In the photoelectric effect, the energy of the photons must be greater than the work function of the material in order to cause the emission of electrons.

3.What is the quantum mechanical explanation for the photoelectric effect?

👉The quantum mechanical explanation for the photoelectric effect is that energy is transferred from photons to electrons in discrete packets called quanta.

4. What did Einstein propose about the energy of a photon and how does it relate to the photoelectric effect?
 👉Einstein proposed that the energy of a photon is directly proportional to its frequency (E = hf). This helps to explain the dependence of the kinetic energy of the emitted electrons on the frequency of the incident radiation in the photoelectric effect.

5.What are some practical applications of the photoelectric effect?
 👉The photoelectric effect has numerous practical applications, such as in solar energy, electronic devices like photodiodes and phototransistors, and in the detection of radiation.

6. Can the photoelectric effect be observed with all types of electromagnetic radiation or only with certain frequencies?
👉The photoelectric effect can only be observed with electromagnetic radiation above a certain frequency, which is determined by the work function of the material.

2.Why can't the photoelectric effect be explained by classical wave theory?

👉The photoelectric effect cannot be explained by classical wave theory because it suggests that the energy from the electromagnetic radiation is transferred continuously to the electrons, which would cause a delay in their emission from the material. However, the photoelectric effect occurs almost instantaneously, suggesting that energy is transferred in discrete packets.

7. What is the significance of the photoelectric effect in the development of quantum mechanics?
 👉The photoelectric effect was one of the key experiments that led to the development of quantum mechanics, as it provided evidence for the concept of quanta and helped to shift the scientific community's understanding of the behavior of light and matter from classical mechanics to quantum mechanics.

8. What is the threshold frequency in the photoelectric effect?
 👉 The threshold frequency is the minimum frequency of the incident radiation that can cause the emission of electrons in the photoelectric effect.

9. What is the work-energy theorem and how does it relate to the photoelectric effect? 
 👉A: The work-energy theorem states that the work done on an object is equal to its change in kinetic energy. In the photoelectric effect, the energy of the photons is equal to the work done on the electrons to remove them from the material. This energy is then converted into the kinetic energy of the emitted electrons.

10. What is the stopping potential in the photoelectric effect? 

A: The stopping potential is the minimum potential difference (voltage) required to stop the flow of electrons emitted in the photoelectric effect. It is related to the maximum kinetic energy of the emitted electrons.

11. Can the photoelectric effect be observed with X-rays?
 👉 A: Yes, the photoelectric effect can be observed with X-rays as well as with other types of electromagnetic radiation.

12. How does the photoelectric effect provide evidence for the particle nature of light? 
  👉A: The photoelectric effect demonstrates that electromagnetic radiation behaves like particles (photons) rather than waves. This provides evidence for the particle nature of light, which was a key development in the history of quantum mechanics.

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Here is more topics cover related to the photoelectric chapter for IOE and also important for class 12 students. Hope this will help you for your exams .  

Dual nature of radiation and matter

Electron.

It is an elementary particle having a negative charge of $1.6\times {10}^{-19} C$ and mass$1.6\times {10}^{-31} Kg$.

Work function.

The minimum amount of energy required by an electron to just escape from the metal surface is known as work function of the metal. It is denoted by W_o.

Electron emission.

The phenomenon of emission of electrons from a metal surface is called electron emission. It is of the following types:

(i) Thermionic emission. Here electrons are emitted from the metal surface with the help of thermal energy.

(ii) Field or cold cathode emission. Electrons are emitted from a metal surface by subjecting it to a very high electric field.

(iii) Photoelectric emission. Electrons are emitted from a metal surface with the help of suitable electromagnetic radiation.

(iv) Secondary emission. Electrons are ejected from a metal surface by striking fast moving electrons over it.

Kinetic energy gained by an electron.

When an electron is accelerated from rest through a potential difference of V volts, the gain in its kinetic energy is

$\mathrm{eV}=\frac{1}{2}{\mathrm{mv}}^2$

Electron volt (eV).

It is the kinetic energy gained by an electron when it is accelerated through a potential difference of 1 volt.

$1 \mathrm{eV} = 1.6\times {10}^{-19} \mathrm{J}$,

$1 \mathrm{MeV} = 1.6\times {10}^{-13} \mathrm{J}$.

The work function of a metal is generally measured in electron volt (eV).

Photons.

According to Planck's quantum theory of radiation, an electromagnetic wave travels in the form of discrete packets of energy called quanta. One quantum of light radiation is called a photon. The main features of photons are as follows:

(i) A photon travels with the speed of light.

(ii) The frequency of a photon does not change as it travels from one medium to another.

(iii) The speed of a photon changes as it travels through different media due to the change in its wavelength.

(iv) The rest mass of a photon is zero i.e., a photon cannot exist at rest.

(v) Energy of a photon, $\mathrm{E}= \mathrm{hv}=\frac{\mathrm{hc}}{\mathrm{\lambda }}$

(vi) Momentum of a photon, $\mathrm{p}= \mathrm{mc} =\frac{\mathrm{hv}}{\mathrm{c}}=\frac{\mathrm{h}}{\mathrm{\lambda }}$

(vii) From Einstein's mass-energy relationship, the equivalent mass m of a photon is given by

$\mathrm{E}= {\mathrm{mc}}^2 =\mathrm{hv} \mathrm{or}$ $\mathrm{m}=\frac{\mathrm{hv}}{{\mathrm{c}}^2}$

Photoelectric effect.

The phenomenon of emission of electrons from a metal surface, when electromagnetic radiations of sufficiently high frequency are incident on it, is called photoelectric effect. The photo (light)-generated electrons are called photoelectrons.

Alkali metals like Li, Na, K, Ce show photoelectric effect with visible light. Metals like Zn, Cd, Mg respond to ultraviolet light.

Photoelectric effect involves the conversion of light energy into electrical energy. It follows the law of conservation of energy. It is an instantaneous process.

Photoelectric current.

The current constituted by photoelectrons is called photoelectric current. Its value depends on:

(i) the intensity of light,

(ii) the potential difference applied between the two electrodes, and 

(iii) the nature of the cathode material.

Cut off or stopping potential.

It is the minimum value of the negative potential that must be applied to the anode of photo-cell to make the photoelectric current zero. It is denoted by Vo. Its value depends on:

(i) the frequency of incident light, and

(ii) the nature of the cathode material.

For a given frequency of incident light, it is independent of its intensity. The stopping potential is directly related to the kinetic energy of the emitted electrons.

${\mathrm{K}}_{\max = \frac{1}{2}{{\mathrm{mv}}^2}_{\max }= {\mathrm{eV}}_{\mathrm{o}}}$

Threshold frequency.

The minimum value of the frequency of incident radiation below which the photoelectric emission stops altogether is called threshold frequency. It is denoted by Vo, and is a characteristic of metal.

Laws of photoelectric effect.

(i) For a given metal and a radiation of fixed frequency, the rate of emission of photoelectrons is proportional to the intensity of incident radiation.

(ii) For every metal, there is a certain minimum frequency below which no photoelectrons are emitted, howsoever high is the intensity of incident radiation. This frequency is called threshold frequency.

(iii) For the radiation of frequency higher than the threshold frequency, the maximum kinetic energy of the photoelectrons is directly proportional to the frequency of incident radiation and is independent of the intensity of incident radiation.

(iv) The photoelectric emission is an instantaneous process.

Failure of wave theory to explain photoelectric effect.

The classical wave theory of radiation could not explain the main features of photoelectric effect. Its picture of continuous absorption of energy from radiation could not explain.

(i) the independence of Kmax on intensity,

(ii) the existence of threshold frequency Vo and

(iii) the instantaneous nature of the phenomenon.

Einstein's theory of photoelectric effect.

Einstein explained photoelectric effect with the help of Planck's quantum theory. When a radiation of frequency v is incident on a metal surface, it is absorbed in the form of discrete packets of energy called quanta or photons. A part of energy hv of a photon is used in removing the electron from the metal surface and remaining energy is used in giving kinetic energy to the photoelectrons. 

Einstein's photoelectric equation is

${\mathrm{K}}_{\max }=\frac{1}{2}{{\mathrm{mv}}^2}_{\max } {\mathrm{eV}}_{\mathrm{o}}= \mathrm{hv}-{\mathrm{W}}_{\mathrm{o}}=\mathrm{h}\left(\mathrm{v}-{\mathrm{v}}_{\mathrm{o}}\right)$

Where wo is the work function of the metal and vo is the threshold frequency.

All the experimental observations can be explained on the basis of Einstein's photoelectric equation.

Compton scattering.

It is the phenomenon of increase in the wavelength of X-ray photons which occurs when these radiations are scattered on striking an electron. Then difference in the wavelength of scattered and incident photons is called Compton shift, which is given by 

$\Delta \lambda =\frac{h}{m_{oc}}(1-\cos \theta )$

Where $\theta$ is the angle of scattering of the X-ray photon and m_o, is the rest mass of the electron

Photocell.

It is an arrangement which converts light energy into electrical energy. It works on the principle of photoelectric effect. It is used in cinematography for the reproduction of sound. Photo-cells are used to operate various control systems and in light measuring devices.

Dual nature of radiation.

Light has dual nature. It manifests itself as a wave in diffraction, interference, polarization, etc., while it shows particle nature in photoelectric effect, Compton scattering, etc.

Dual nature of matter.

As there is complete equivalence between matter (mass) and radiation (energy) and the principle of symmetry is always obeyed, de Broglie suggested that moving particles like protons, neutrons, electrons, etc. should be associated with waves known as de Broglie waves and their wavelength is called de Broglie wavelength. The de Broglie wavelength of a particle of mass m with velocity v is given by

$\mathrm{\lambda }=\frac{\mathrm{h}}{\mathrm{p}}=\frac{\mathrm{h}}{\mathrm{mv}}$

Where h is the Planck's constant. The de Broglie wavelength is independent of the charge and nature of the material particles. It has significantly measurable values for sub-atomic particles like electrons, protons, etc., due to their small masses. For macroscopic objects of everyday life, the de Broglie wavelength is extremely small, quite beyond measurement.

de Broglie wavelength of an electron.

The wavelength associated with an electron beam accelerated through a potential difference of V volts is given by

$h=\frac{h}{\sqrt{2meV}}=\frac{1.227}{\sqrt{V}}nm.$

Read More : 

1. Wave Motion

2. Polarization 

.3. Heat and Temperature for IOE

4. Antiderivatives