Question

When 40 kV is applied across an X-ray tube, X-ray is obtained with a maximum frequency of 9.7 × 10¹⁸ Hz. Calculate the value of Planck constant from these data.

Answer 1

Given:
Potential applied to the X-ray tube, V = 40 kV
Frequency of the X-ray, v = 9.7 × 10¹⁸ Hz
Wavelength $\left(\lambda \right)$ is given by
$\lambda =\frac{hc}{eV}$
Here,
h = Planck's constant
c = Speed of light
e = 1.6 $\times$ 10^$-19$
$$\begin{gathered} \therefore \lambda =\frac{hc}{e\mathrm{V}} \\ \Rightarrow \frac{\lambda }{c}=\frac{h}{eV} \\ \Rightarrow \frac{1}{v}=\frac{h}{eV}\left(\because v=\frac{c}{\lambda }\right) \\ \Rightarrow h=\frac{eV}{v} \\ \Rightarrow h=\frac{40\times {10}^3}{9.7\times {10}^{18}}\times e \\ \Rightarrow h=4.12\times {10}^{-15}e\mathrm{Vs} \end{gathered}$$