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Question
The ground state energy of hydrogen atoms is -13.6 eV. The photon emitted during the transition of electron from n = 3 to n = 1 unknown work function. The photoelectrons are emitted from the material with a maximum kinetic energy of 9 eV. Calculate the threshold wavelength of the material used.
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Solution
For a transition from n = 3 to n = 1 state, the energy of the emitted photon,
hv = E2 – E1 = `13.6[1/1^2 - 1/3^2]` eV = 12.1 eV.
From Einstein’s photoelectric equation,
hv + Kmax + W0
∴ W0 = hv – Kmax = 12.1 – 9 = 3.1 eV
Threshold wavelength,
λth = `("hc")/"W"_0`
= `(6.62 xx 10^-34 xx 3 xx 10^8)/(3.1 xx 1.6 xx 10^-19)`
= 4 × 10–7m
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