A mercury lamp is a convenient source for studying the frequency dependence of photoelectric emission since it gives a number of spectral lines ranging from the UV to the red end of the visible spectrum. In our experiment with rubidium photo-cell, the following lines from a mercury source were used: $\lambda_{1}=3650 \AA$ $\lambda_{2}=4047 \AA$ $\lambda_{3}=4358 \AA$ $\lambda_{4}=5461 \AA$, $\lambda_{5}=6907 \AA$. The stopping voltages, respectively, were measured to be: $\mathbf{V}_{01}=1.28 \mathrm{~V}, \mathrm{~V}_{02}=0.95 \mathrm{~V}, \mathrm{~V}_{03}=0.74 \mathrm{~V}$, $\mathrm{V}_{04}=0.16 \mathrm{~V}, \mathrm{~V}_{05}=0 \mathrm{~V}$.Determine the value of Planck's constant $\mathrm{h}$, the threshold frequency and work function for the material.

A mercury lamp is a convenient source for studying the frequency dependence of photoelectric emission since it gives a number of spectral lines ranging from the UV to the red end of the visible spectrum. In our experiment with rubidium photo-cell, the following lines from a mercury source were used:
$\lambda_{1}=3650 \AA$ $\lambda_{2}=4047 \AA$ $\lambda_{3}=4358 \AA$ $\lambda_{4}=5461 \AA$ , $\lambda_{5}=6907 \AA$ . The stopping voltages, respectively, were measured to be: $\mathbf{V}_{01}=1.28 \mathrm{~V}, \mathrm{~V}_{02}=0.95 \mathrm{~V}, \mathrm{~V}_{03}=0.74 \mathrm{~V}$ , $\mathrm{V}_{04}=0.16 \mathrm{~V}, \mathrm{~V}_{05}=0 \mathrm{~V}$ .Determine the value of Planck’s constant $\mathrm{h}$ , the threshold frequency and work function for the material.

CBSE | Class 12 | Dual Nature of Radiation and Matter | NCERT | Physics

The following relation can be derived from photoelectric effect,
$eV_{o}=hv-\phi_{o}$

Work function of the metal, $\Phi_{0}=\mathrm{hv}-\mathrm{eV}_{0}$

$\Phi_{0}=(h c / \lambda)-e V_{0}$

$V_{0}=\frac{h}{e} \nu-\frac{\phi_{0}}{e}---(1)$

Here,

$\mathrm{V}_{0}$ is the Stopping potential
$\mathrm{h}$ is the Planck’s constant
$\mathrm{e}$ is the Charge on an electron
$\mathrm{v}$ is the Frequency of radiation

$\Phi_{0}$ is the Work function of a material

As we know, stopping proportional is directly proportional to the frequency from the relation,

Frequency, $v=$ Speed of light $(c) /$ Wavelength $(\lambda)$

Using this above equation, we can calculate the frequency of various lines

$v_{1}=c/\lambda_{1}=3 \times 10^{8} / 3650 \times 10^{-10}$

$=8.219 \times 10^{14} \mathrm{~Hz}$

$v_{1}=c/\lambda_{2}=3 \times 10^{8} / 4047 \times 10^{-10}$

$=7.412 \times 10^{14} \mathrm{~Hz}$

$v_{1}=c/\lambda_{3}=3 \times 10^{8} / 4358 \times 10^{-10}$

$=6.88 \times 10^{14} \mathrm{~Hz}$

$v_{1}=c/\lambda_{4}=3 \times 10^{8} / 5461 \times 10^{-10}$

$=5.493 \times 10^{14} \mathrm{~Hz}$

$v_{1}=c/\lambda_{5}=3 \times 10^{8} / 6907 \times 10^{-10}$

$=4.343 \times 10^{14} \mathrm{~Hz}$

The above values can be plotted in a graph

A straight line can be seen in the graph. At $5 \times 10^{14} \mathrm{~Hz}$ , it crosses the y-axis. This is the frequency at which the threshold is reached. The frequency less than the threshold frequency is represented by point D.