The de Broglie wavelength associated with the kinetic energy k is given as \(\lambda=\frac{h}{\sqrt{2 m k}}\) , where m is the mass of the particle.
Therefore \(\lambda_{\mathrm{e}}=\frac{\mathrm{h}}{\sqrt{2 \mathrm{~m}_{\mathrm{e}} \mathrm{k}_{\mathrm{e}}}} \text { and } \lambda_{\alpha}=\frac{\mathrm{h}}{\sqrt{2 \mathrm{~m}_{\alpha} \mathrm{k}_{\alpha}}} \text {. But } \mathrm{k}_{\mathrm{e}}=\mathrm{k}_{\alpha} . \)
Therefore \(\frac{\lambda_{\mathrm{e}}}{\lambda_{\alpha}}=\sqrt{\frac{\mathrm{m}_{\alpha}}{\mathrm{m}_{\mathrm{e}}}} \mathrm{m}_{\alpha}>\mathrm{m}_{\mathrm{e}^{*}} \text {. Therefore, } \lambda_{\mathrm{e}}>\lambda_{\alpha^{\circ}}\)

de Broglie wavelength \(\lambda=\frac{\mathrm{h}}{\mathrm{mv}}\)
Kinetic energy of electron K \(=\frac{1}{2} m v^{2} \text { (or) } v=\sqrt{\frac{2 K}{m}}\)
Now de Broglie wavelength is \(\lambda=\frac{h}{m v}=\frac{h}{m \sqrt{2 K / m}} \)
\(\lambda=\frac{h}{\sqrt{2 m K}} \)

The de Broglie wavelength associated with the kinetic energy K is \(\lambda=\frac{h}{\sqrt{2 m k}}\)
Where m is the mass of the particle
Since proton and electron have same KE, the wavelength is inversely proportional to square root of the mass \(\lambda \alpha \frac{1}{\sqrt{m}}\)
Mass of proton is 1840 times greater them that of electron. Therefore, de Broglie's wavelength of electron is greater than the proton.

Due to the large mass of a baseball, the de Broglie wavelength (⋋ = h/mv) associated with a moving baseball is very small. Hence, its wave nature is not visible.

According to de Broglie hypothesis, if radiation has a dual nature, then the moving particles of matter Iike electrons, protons, neutrons in motion should exhibit wave like character under an appropriate conditions. These waves are called de Broglie waves or matter waves.

Photo cell is a device which converts light energy into electrical energy. It works on the principle of photo electric effect. When light is incident on photosensitive materials, their electric properties will get affected, based on which Photo cells are classified into three types. They are
(i) Photo emissive cell
(ii) Photo voltaic cell
(iii) Photo conductive cell

For a given metallic Surface, the emission of photo electrons takes place only if the frequency of incident light is greater than a certain minimum frequency called the threshold frequency.

According to quantum concept, intensity of light of given wavelength is defined as the number of energy quanta or photons incident per unit area per unit time, with each photon having same energy. Its unit is Wm^-2.

The photocurrent, (ie. the number of electrons emitted per second) is directly proportional to the intensity of the incident light.

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.

\(\text { (i) } \lambda_{\mathrm{d}}=\frac{\mathrm{h}}{\sqrt{2 \mathrm{meV_1}}} ; \lambda_{\alpha}=\frac{\mathrm{h}}{\sqrt{\mathrm{me}}}\)
\(\frac{\lambda_{\mathrm{d}}}{\lambda_{\alpha}}=\frac{\frac{1}{\sqrt{2 m e}}}{\frac{1}{\sqrt{4 m 2 e}}} \Rightarrow \lambda_{\mathrm{d}}=2 \lambda_{\alpha}\)
\(\text { (ii) } =\frac{K.E_d}{K.E_a}=\frac{eV}{2eV} =\frac{1}{2}\Rightarrow K.E_d=\frac{1}{2}K.E_a\)
∴ K.E of deuteron is half of K.E of α-particle.

(i) Davisson - Germer experiment
(ii) Diffraction phenomenon