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Monochromatic radiation emitted when electron on hydrogen atom jumps from first excited to the ground state irradiates a photosensitive material. The stopping potential is measured to be 3.57 V. The threshold frequency of the material is
A
$2.5\times10^{15}$ Hz
B
$4\times10^{15}$ Hz
C
$5\times10^{15}$ Hz
D
$1.6\times10^{15}$ Hz
Detailed Solution
Photon energy for n = 2 → n = 1: $E = 13.6\left(1 - \frac{1}{4}\right) = 10.2$ eV
Einstein's equation: $eV_0 = E - h\nu_{th}$
$h\nu_{th} = 10.2 - 3.57 = 6.63$ eV $= 6.63\times1.6\times10^{-19}$ J
$\nu_{th} = \frac{6.63\times1.6\times10^{-19}}{6.6\times10^{-34}} \approx 1.6\times10^{15}$ Hz
Einstein's equation: $eV_0 = E - h\nu_{th}$
$h\nu_{th} = 10.2 - 3.57 = 6.63$ eV $= 6.63\times1.6\times10^{-19}$ J
$\nu_{th} = \frac{6.63\times1.6\times10^{-19}}{6.6\times10^{-34}} \approx 1.6\times10^{15}$ Hz