JEE Advanced · 2023 · 04 Jun 2023 · Paper 1 · Modern Physics

A Hydrogen-like atom has atomic number

Z

. Photons emitted in the electronic transitions from level

n = 4

to level

n = 3

in these atoms are used to perform photoelectric effect experiment on a target metal. The maximum kinetic energy of the photoelectrons generated is 1.95 eV. If the photoelectric threshold wavelength for the target metal is 310 nm, the value of

Z

is ____.
[Given:

h c = 1240 eV - nm

and

R h c = 13.6 eV

, where

R

is the Rydberg constant,

h

is the Planck's constant and

c

is the speed of light in vacuum]

Answer: 3

Solution

Energy of photon emitted in transition from

n = 4

n = 3

E = 13.6 Z^{2} (\frac{1}{3 ^{2}} - \frac{1}{4 ^{2}}) = 13.6 Z^{2} (\frac{1}{9} - \frac{1}{16}) = 13.6 Z^{2} \times \frac{7}{144} = 0.66 Z^{2}

eV

Work function of metal:

W = \frac{h c}{λ} = \frac{1240}{310} = 4

eV

Photoelectric equation:

K_{ma x} = E - W

1.95 = 0.66 Z^{2} - 4

0.66 Z^{2} = 5.95

Z^{2} = 9

Z = 3

JEE Advanced · 2023 · 04 Jun 2023 · Paper 1 · Integer answer

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JEE Advanced · 2023 · 04 Jun 2023 · Paper 1 · Modern Physics

Solution

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