\(\lambda\propto \frac{1}{\sqrt{V}}\)
\(\frac{\lambda_1}{\lambda_2}=\frac{\sqrt{224\times10^3}}{\sqrt{14\times 10^3}}\)
\(=\sqrt{16}=4\)
\(\lambda_{\mathrm{2}}= \frac{\lambda_1}{4}\)

\(\mathrm{E}_{\mathrm{p}}  =\frac{\mathrm{hc}}{\lambda_{\mathrm{p}}}  \)
\(\mathrm{E}_{\mathrm{e}}  =\frac{\mathrm{h}^2}{2 \mathrm{~m} \lambda_{\mathrm{e}}^2}  \)
\(\frac{\mathrm{hc}}{\lambda_{\mathrm{p}}}  =\frac{\mathrm{h}^2}{2 \mathrm{~m} \lambda_{\mathrm{e}}^2}  \)
\(\lambda_{\mathrm{p}}  \propto \lambda_{\mathrm{e}}^{{ }^2}\)

(i) Metals like cadmium, zinc, magnesium, alkali metals lithium, sodium, caesium respond to visible light.
(ii) The materials which eject photoelectrons upon irradiation of electromagnetic wave of suitable wavelength are called photosensitive materials.

The potential barrier which prevents free electrons from leaving the metallic surface is called surface barrier.

V = 81 V
∴ K = eV = 1.6 x 10^-19 x 81 = 1.296 x 10^-17 = 1.3 x 10^-17 J
\({ V }=\sqrt \frac {2K}{m}\sqrt { \cfrac { 2\times 1.3\times { 10 }^{ -17 } }{ 9.1\times { 10 }^{ -31 } } } =5.345 \times 10^6 ms^{-1} \) 
v = 5.345 x 10⁶ m s^-1, K = 1.3 x 10^-17 J

P = 50 mW; λ = 640nm = 640 x 10^-9 m
P = 50 x 10^-3W
\(n=\cfrac { hc }{ \lambda } = \frac{6.626 \times10^{-34} \times 3 \times 10^8}{640 \times 10{-9}}=3.106 \times 10^{-19}J\)
\(n=\frac{E}{hv}=\cfrac { 50\times { 10 }^{ -3 } }{ 3.106\times { 10 }^{ -19 } } = 1.61\times 10^{17} s^{-1}\) 
n = 1.61 x 10¹⁷ s^-I

The ejection of electrons from the metal plate when illuminated by light or any electromagnetic radiation of suitable wavelength (or frequency) is called photoelectric effect.

The minimum energy needed for an electron to escape from the metal surface is called work function of that metal.
Unit: electron volt (eV).

In metals, the electrons in the outer most shells are loosely bound to the nucleus. Even at room temperature, these large number of electrons which are moving inside the metal in random manner and they cannot leave the surface of metal. So that metals have a large number of free electrons.

(i) In metals, the electrons in the outer most shells are loosely bound to the nucleus. Even at room temperature, there are a large number of free electrons which are moving inside the metal in a random manner. Through they move freely inside the metal they cannot leave the surface of the metal. The reason is that when free electrons reach the surface of the metal they are attracted by the positive nuclei of the metal. It is attractive pull which will not allow free electrons to leave the metallic surface at room temperature.
(ii) In order to leave the metallic surface, the free electrons must cross a potential barrier created by the positive nuclei of the metal. The potential barrier. which prevents free electrons from leading the metallic surface is called surface barrier.
(iii) Whenever an additional energy is given to the free electrons, they will have sufficient energy to cross the surface barrier. And they escape from the metallic surface. The liberation of electrons from any surface of a substance is called electron emission.
(iv) The minimum energy needed for an electron to escape from the metal surface is called work function of that metal.
(a) Thermionic emission
(i) When a metal is heated to a high temperature, the free electrons on the surface of the metal get sufficient energy in the form of thermal energy so that they are emitted from the metallic surface. This type of emission is known a thermonic emission.

(ii) The intensity of the thermionic emission (the number of electrons emitted) depends on the metal used and its temperature.
(iii) Examples: cathode ray tubes, electron microscopes, X-ray tubes etc.

(b) Field emission
(i) Electric field emission occurs when a very strong electric field is applied across the metal.
(ii) This strong field pulls the free electrons and helps them to overcome the surface barrier of the metal.
(iii) Ex: Field ermssion scanning electron microscopes, Field-emission display etc.

(c) Photo electric emission
(i) When an electromagnetic radiation of suitable frequency is incident on the surface of the metal, the energy is transferred from the radiation to the free electrons.
(ii) Hence, the free electrons get sufficient energy to cross the surface barrier and the photo electric emission takes place.
(iii) The number of electrons emitted depend on the intensity of the incident radiation.
(iv) Examples: Photo diodes, photo electric cells etc. 

(d) Secondary emission
(i) When a beam of fast-moving electrons strikes the surface of the metal, the kinetic energy of the striking electrons is transferred to the free electrons on the metal surface.
(ii) Thus the free electrons get sufficient kinetic energy so that the secondary emission of electron occurs.
(iii) Examples: Image intensifiers, photo multiplier tubes etc.

Photo sensitive material - Carbon

(a)  Assertion and Reason are correct and Reason is the correct explanation of Assertion.

I, II and III only

I, II, III and IV

(i) Photo cells are used as switches and sensors.
(ii) Automatic switch on and off of street lights.
(iii) They are used for reproduction of sound in motion pictures
(iv) They are used as timers to measure the speed of athletes during a race.
(v) In photography, they are used to measure the intensity of the given light and to calculate the exact time of exposure.

1) The frequency of incident radiation was kept constant.
2) de Broglie wavelength,
\(\lambda =\frac { h }{ \sqrt { 2mqV } } \alpha \frac { 1 }{ V } \)
If potential difference V is doubled, the de-Broglie wavelength is decreased to \(\frac { 1 }{ \sqrt { 2 } } \) time.