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State Einstein’s photoelectric equation explaining the symbols used.

Light of frequency $\nu$ incident is on a photosensitive surface. A graph of the square of the maximum speed of the electrons $\left ( V^{2}_{max} \right )VS$ . $\nu$ is obtained as shown in the figure.

Using Einstein’s photoelectric equation, obtain expressions for

(i) Planck’s constant
(ii) work function of the given photosensitive material in terms of parameters $l,n$ and mass of the electron m.

Answers (1)

Einstein's photoelectric equation.

$KE_{max}=h\nu -\phi _{0}$

Where,

$KE_{max}$ is the maximum kinetic energy of the emitted photon.

$\phi _{0}=$ The work function of the material

$\nu =$ frequency of incident light

$h=$ planks constant

From Einstein's photoelectric equation

$KE_{max}=h\nu -h\nu _{0}$

$\frac{1}{2}mV^{2}_{max}=\left ( \frac{2h}{m} \right )\nu -\left ( \frac{2h}{m} \right )\nu _{0}$

From the given graph

$\frac{2h}{m}=\frac{l}{n}$

(i) Planks constant :

$h=\frac{lm}{2n}$

(ii) Work function

$\phi =h\nu _{0}$

from graph

$\nu _{0}=n$

$\phi =hn$

$h=\frac{lm}{2n}\Rightarrow \phi =\frac{lm}{2n}\times n$

$\phi =\frac{lm}{2}$

Posted by

Safeer PP

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