Question

The stopping potential in a photoelectric experiment is linearly related to the inverse of the wavelength (1/λ) of the light falling on the cathode. The potential difference applied across an X-ray tube is linearly related to the inverse of the cutoff wavelength (1/λ) of the X-ray emitted. Show that the slopes of the lines in the two cases are equal and find its value.

Answer 1

The value of line slopes in two cases is $1.242 \times 10-6 \mathrm{Vm}$.

Explanation:

Stopping potential is denoted as $V_{0}$.

Across the x-ray tube, the potential difference is shown as K.

Wavelength and cut difference wavelength are shown as λ.

$\mathrm{eV} 0=\mathrm{hf}-\mathrm{hf} 0 \lambda$

$=\mathrm{hceer} \mathrm{Vo} \lambda=\mathrm{hce}$

It is to be observed that the slopes are equal here, that is, $\mathrm{V}_{0} \lambda=\mathrm{y} \lambda$

$\text { hce }=6.63 \times 3 \times 10-34 \times 1081.6 \times 10-19=1.242 \times 10-6 \mathrm{Vm}$.