EINSTEIN'S PHOTOELECTRIC EQUATION: ENERGY QUANTUM OF RADIATION -

in 1905 Albert Einstein proposed a radically new picture of electromagnetic radiation to explain the photoelectric effect. In this picture, radiation energy is built up to discrete units- the so-called quanta of the energy of radiation (photon).

Each quantum of radiant energy has energy

$\fn_jvn \left [ E=h\nu \right ]$

where $\fn_jvn h-plank \;constant\;(6.62\times10^{-34}js)$

$\fn_jvn \nu-frequency\;of\;radiation$

In the photoelectric effect, each electron absorbs a quantum of energy of radiation. If this quantum of energy absorbed exceeds the minimum energy needed for the electron to escape from the metal surface (work function), the electron is emitted with maximum K.E

$\fn_jvn \left [ K_{max}=h\nu-\Phi_0 \right ]$

More tightly bound electrons will emerge with K.E less than the maximum value.

The above equation is known as Einstein’s photoelectric equation.

$\fn_jvn \left [ K_{max}=h\nu-\Phi_0 \right ]$ ——————————(1)

if max K.E is zero, then, in this case, electrons may just come out.

i.e $\fn_jvn K_{max}=0$

$\fn_jvn \Rightarrow h\nu-\Phi_0=0$

$\fn_jvn \left [ \nu=\frac{\Phi_0}{h} \right ]$

This frequency is known as Threshold frequency and denoted by $\fn_jvn \nu_0$

$\fn_jvn \left [ \nu_0=\frac{\Phi_0}{h} \right ]$ —————————–(2)

i.e photoelectric emission is possible only if $\fn_jvn K_{max}\geqslant 0$

$\fn_jvn \Rightarrow h\nu-\Phi_0\geqslant 0$

$\fn_jvn \Rightarrow \nu\geqslant \frac{\Phi_0}{h}$

$\fn_jvn \left [ \nu\geqslant \nu_0 \right ]$

from (1) and (2), we can write

$\fn_jvn \Rightarrow K_{max}=h\nu-h\nu_0$

$\fn_jvn \left [ K_{max}=h(\nu-\nu_0) \right ]$

The corresponding wavelength of threshold frequency is known as the Threshold wavelength.

$\fn_jvn \left [ K_{max}=h\left ( \frac{c}{\lambda}-\frac{c}{\lambda_0} \right ) \right ]$

where $\fn_jvn \lambda_0$ – Threshold wavelength

NOTE:-

(1) From equation (2) for higher work function of metal higher the threshold frequency.

(2) We know that

$\fn_jvn K_{max}=e V_0$

Therefore from the photoelectric equation, we can write

$\fn_jvn K_{max}=h\nu-\Phi_0$

$\fn_jvn \Rightarrow e V_0=h\nu-\Phi_0$

$\fn_jvn \left [ V_0=\left ( \frac{h}{e} \right )\nu-\frac{\Phi_0}{e} \right ](look\;like\;\; y=mx+c)$

It predicts that the curve is a straight line with a slope . $\fn_jvn m=\frac{h}{e}$

IMPORTANT LINKS OF WAVE OPTICS
Introduction	Electron Emission
Photoelectric Effect	Experimental Study of Photoelectric Effect
Photoelectric Effect and Wave Theory of Light	Einstein’s Photoelectric Equation: Energy Quantum of Radiation
Particle Nature of Light: The Photon	Wave Nature of Matter
Davisson and Germer Experiment