JEE Main 2020 · Physics · Atoms, Nuclei and Dual Nature of Radiation · medium

In a photoelectric experiment the stopping potential is 2.0 V for light of wavelength 310 nm and 3.0 V for light of wavelength 248 nm. Without using…

Numerical answer

In a photoelectric experiment the stopping potential is

2.0\ \mathrm{V}

for light of wavelength

310\ \mathrm{nm}

and

3.0\ \mathrm{V}

for light of wavelength

248\ \mathrm{nm}

. Without using any value of

h

c

separately, find the threshold wavelength of the metal (in nm).

Show answer and solution

Answer: 620

Einstein's equation:

eV_0 = \dfrac{hc}{\lambda} - \phi

. Subtracting the two cases:

e(3.0 - 2.0) = hc\left(\dfrac1{248} - \dfrac1{310}\right)

, so

hc/e = \dfrac{1.0}{8.065\times10^{-4}} = 1240\ \mathrm{V\,nm}

. Then

\phi/e = \dfrac{1240}{310} - 2.0 = 4.0 - 2.0 = 2.0\ \mathrm{V}

. The threshold wavelength is

\lambda_0 = \dfrac{hc}{\phi} = \dfrac{1240}{2.0} = 620\ \mathrm{nm}

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