An electron and proton are separated by a large distance. The… | JEE Main 2021 (27 Jul, Shift 2)

Q6JEE Main 2021 · 27 JUL · SHIFT 2Difficult

Other / Mixed: Atoms & Bohr Links

An electron and proton are separated by a large distance. The electron starts approaching the proton with energy 3 eV. The proton captures the electron and forms a hydrogen atom in second excited state. The resulting photon is incident on a photosensitive metal of threshold wavelength 4000 $\text{\AA}$ . What is the maximum kinetic energy of the emitted photoelectron?

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Answer: (b)

Second excited state is $n = 3$ : $E_3 = -\frac{13.6}{9} = -1.51\text{ eV}$ .
Photon energy $= 3 + 1.51 = 4.51\text{ eV}$
Work function $\phi = \frac{12400}{4000} = 3.1\text{ eV}$
$K_{max} = 4.51 - 3.1 = 1.41\text{ eV}$
So the answer is (b) 1.41 eV.

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