Question:
In an experiment on photoelectric effect, the slope of the cut-off voltage versus frequency of incident light is found to be $4.12 \times 10^{-15} \mathrm{Vs}$. Calculate the value of Planck's constant.
Solution:
The slope of the cut-off voltage (V) versus frequency (ν) of an incident light is given as:
$\frac{V}{V}=4.12 \times 10^{-15} \mathrm{Vs}$
$V$ is related to frequency by the equation:
$h v=e V$
Where,
e = Charge on an electron = 1.6 × 10−19 C
h = Planck’s constant
$\therefore h=e \times \frac{V}{v}$
$=1.6 \times 10^{-19} \times 4.12 \times 10^{-15}=6.592 \times 10^{-34} \mathrm{JS}$
Therefore, the value of Planck's constant is $6.592 \times 10^{-34} \mathrm{Js}$.