Question

In a historical experiment to determine Planck's constant, a metal surface was irradiated with light of different wavelengths. The emitted photoelectron energies were measured by applying a stopping potential. The relevant data for the wavelength ($\lambda$) of incident light at the corresponding stopping potential ($V_0$) are given below:

$\lambda \left(\mu m\right)$	$V_0$ (Volt)
0.3	2.0
0.4	1.0
0.5	0.4

Given that $c=3\times {10}^{8}m{s}^{-1}$ and $e=1.6\times {10}^{-19}C$, Planck's constant (in units of J s) from such an experiment is :

• A. $6.0\times {10}^{-34}$
• B. $6.4\times {10}^{-34}$
• C. $6.6\times {10}^{-34}$
• D. $6.8\times {10}^{-34}$

Answer 1

The correct option is B $6.4\times {10}^{-34}$

$\frac{hc}{\lambda }-\varphi =e{V}_0$

From given data,

$\frac{hc}{0.3X{10}^{-6}}-\varphi =2e$

$\frac{hc}{0.4X{10}^{-6}}-\varphi =e$

Subtracting, we get,

$hc(\frac{1}{0.3}-\frac{1}{0.4}){10}^6=e$

$h=6.4\times {10}^{-34}Js$

Answer is option B.