\(\lambda =\frac { h }{ \sqrt { 2mqV } } ;\lambda '=\frac { h }{ \sqrt { 3\times 2meV } } \)
\(\frac { \lambda ' }{ \lambda } =\frac { 1 }{ \sqrt { 3 } } \quad \frac { \lambda }{ \sqrt { 3 } } \)

de Broglie wavelength \(\lambda =\frac { P }{ m } \propto \frac { 1 }{ m } \) for the same velocity v.
\(\frac { { \lambda }_{ p } }{ { \lambda }_{ d } } =\frac { { m }_{ d } }{ { m }_{ p } } =\frac { 2{ m }_{ p } }{ { m }_{ p } } =\frac { 2 }{ 1 } \) = 2.1

Davisson-Germer experiment was performed to verify wave nature of electrons. It is the first experimental evidence for wave nature of matter.

The amount of light energy or photon energy incident per meter square per second is called the intensity of radiation.
SI unit: \(\frac { W }{ { m }^{ 2 } } \) or J/s-m².

Maximum kinetic energy, (E_k)_max = eVs = e(2V) = 2eV

The minimum retarding (negative) potential of anode of a photoelectric tube fro which photoelectric current stops or becomes zero is called the stopping potential.

The resistance of the semiconductor changes in accordance with the radiant energy incident on it.

(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.

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 \(\frac{\lambda_{\mathrm{e}}}{\lambda_{\alpha}}=\sqrt{\frac{\mathrm{m}_{\alpha}}{\mathrm{m}_{\mathrm{e}}}} \mathrm{m}_{\alpha}>\mathrm{m}_{\mathrm{e}^{*}} \text {. Therefore, } \lambda_{\mathrm{e}}>\lambda_{\alpha^{\circ}}\)

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.

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

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

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