According to the dual nature of radiation and matter NCERT solutions, electron emission is defined as the process of electrons emitting from a metal surface when it absorbs a certain amount of energy. This is due to the presence of negatively charged free electrons on the metal surface, present in the outermost/ valence shell that is loosely bound to the positively charged nucleus.

There are 3 types of electron emission:

• Thermionic emission
• Field emission
• Photoelectric emission

Dual nature of radiation and matter NCERT solutions explains the photoelectric effect as the phenomenon of electron emission from the surface of a metal when light radiations of suitable frequency fall on it. This phenomenon was discovered by Hertz.

Threshold frequency: When the frequency of light incident is less than a certain minimum value, no electrons are emitted.

The following are the results of the experiment on the photoelectric effect:

• The intensity of incident light has a direct relationship with the photoelectric current.
• If the intensity of the radiation rises, the saturation current increases.
• The intensity of light has no bearing on stopping potential.
• The frequency of incoming light has a linear relationship with the stopping potential and maximal kinetic energy of photoelectrons.

Dual nature of radiation and matter NCERT solutions enumerates the following steps involved in the experiment conducted by Hertz to prove this phenomenon in a clear and diagrammatic manner:

• While generating electromagnetic waves by spark discharge, the sparks around the detector loop intensify when ultraviolet radiation falls on the emitter plate.
• The valence electrons receive enough energy from the radiation falling on the metal surface to overcome the attraction of positive ions and escape from the metal, intensifying the sparks across the metal loop.

The observations are as follows:

• When the photoelectric current measurements were plotted against various light intensity levels, a straight line passing through the origin was seen.
• It was established that photoelectric current, or the number of photoelectrons flowing per unit time is proportional to incoming light intensity.

Based on these, the following cases can be individually studied:

• When the collection plate was held at a greater potential than the emitter (accelerating potential).
• When the collection plate was held at a lower potential than the emitter (retarding potential).
• For three distinct levels of incoming light intensity, the fluctuation of photoelectric current was plotted versus the potential (keeping the frequency constant).

The following are the inconsistencies of the wave theory with the experiments conducted for the photoelectric effect:

• According to wave theory, changes in intensity should influence the photoelectron's maximal kinetic energy. However, investigations on the photoelectric effect revealed that maximal kinetic energy remains unaffected by intensity changes.
• The relationship between stopping potential and threshold frequency was not discussed in wave theory. It stated that the only way to overcome the halting potential was to increase the intensity.
• According to the wave hypothesis, the photoelectric effect was a time-consuming process rather than an instantaneous one.

According to Einstein, radiation comprises specific and discrete packets of energy termed as quanta of radiation energy.

The value of each energy quantum is the same as hv.

Here:

• h = Planck’s constant
• v = frequency of incident light

The following cases should be considered:

• Case-1: hv < Φo (Energy of photon is less than the work function of metal), no photoelectric emission occurs
• Case-2: hv = Φo) (Energy of photon is exactly the same as the work function of metal), electrons get enough energy to just escape the metal surface.
• Case-3: hv > Φo (Energy of photon is greater than the work function of metal)

hv = Φo + Kmax, where Kmax is the maximum kinetic energy of a photoelectron.

About photons:

• Photons of identical frequencies possess the same energies and momentums
• Photons are electrically neutral

Wave-particle dualism:

• The photoelectric effect proves the particle nature of radiation.
• The wave of nature is verified by phenomena such as interference, diffraction, and polarization.

Hence, radiation displays both wave nature and particle nature.

• According to De Broglie, if radiation can possess dual nature, matter can also possess dual nature.
• A particle of mass (m), moving with velocity (v) can behave like a wave under suitable conditions.
• The corresponding wave related to that matter is called matter wave.
• De Broglie’s wavelength for matter wave: λ = h/p

Monochromatic light of wavelength 632.8nm is generated by a helium-neon laser having a power of 9.42mW. Evaluate the following:

• Energy and momentum of each photon
• The number of photons emitted per second
• The speed of a hydrogen atom to have momentum equal to that of an emitted photon by the laser.

Answer:

Given, λ = 632×10-9nm, P = 9.42×10-3W

1. Energy of a photon is given by: E = hv = hc/λ

E = 6.6 x 10-34 3 x 108 / 632.8 x 10-9 = 3.12 x 10-19 J = 3.13 eV

Momentum of the photon is given by: p = hv/c = h/λ

P = 6.6 x 10-34 3 x 108 / 632.8 x 10-9 = 1.043 x 10-27 kg/ms

b. Number of photons emitted per second (n) will be given by the equation:

Power = n × energy of a photon

9.42×10-3 W = n × 3.13×10-19 J

To find the speed of a hydrogen atom (v) to have momentum same as a photon:

v = p/m

Here, p = momentum of photon = 1.043×10-27 kgm/s, and

M = mass of a hydrogen atom which is equal to 1.67×10-24kg

1. What is the nature of radiation?

When radiation travels through an aperture or an edge, it has the property of bending. Only if the radiation has a wave character can it be bent. Radiation beams or rays change direction when they strike a reflecting surface or an optically denser medium, as seen by reflection and refraction. It doesn't explain the radiations' particle nature. The photoelectric effect of radiation states that when a photon of radiation collides with a metal surface, if the photon's energy is above the metal's threshold energy, electrons are emitted. Radiations are shown as a packet of energy or a particle with one phonon energy in this effect. Hence, the properties of photoelectric effect and diffraction explain the dual nature of radiation.

2. What were the observations made by Hertz and Lenard on the photoelectric effect?

As mentioned in dual nature of radiation and matter class 12 NCERT solutions, in 1887, Heinrich Hertz discovered that when light falls on a metal surface, certain electrons near the surface absorb enough energy from the incoming radiation to overcome the attraction of the positive ions in the surface material.

3. How many subtopics are included in the dual nature of radiation and matter chapter of class 12 physics?

The following are the subtopics in dual nature NCERT solutions:

1. Introduction
2. Electron Emission
3. Photoelectric Effect
4. Hertz’s observations
5. Hallwachs’ and Lenard’s observations
6. Experimental Study Of Photoelectric Effect
7. Effect of intensity of light on photocurrent
8. Effect of potential on photoelectric current
9. Effect of frequency of incident radiation on stopping potential
10. Photoelectric Effect and Wave Theory of Light Ex
11. Einstein’s Photoelectric Equation: Energy Quantum of Radiation
12. Particle Nature of Light: The Photon
13. Wave Nature of Matter

4. What is the photoelectric effect in Chapter 11 of NCERT Solutions for Class 12 Physics?

As mentioned in NCERT solutions for class 12 physics chapter 11, the photoelectric effect is the phenomenon of electrons emitting from a metal's surface when a sufficient frequency of light falls on it.

Other related concepts given in dual nature of matter and radiation NCERT solutions include the following:

• Photoelectrons are expelled electrons.
• The photocurrent is the current generated by released electrons.