Hydrogen atom is bombarded with electrons accelerated through a potential different of V, which causes excitation of hydrogen atoms. If the experiment is being formed at \(\mathrm{T}=0 \mathrm{~K}\). The minimum potential difference needed to observe any Balmer series lines in the emission spectra will be \(\frac{\alpha}{10} \mathrm{~V}\), where \(\alpha=\) ______.

JEE Main · 2024 · 29 Jan 2024 · Shift 2 · Modern Physics

Hydrogen atom is bombarded with electrons accelerated through a potential different of V, which causes excitation of hydrogen atoms. If the experiment is being formed at

T = 0 K

. The minimum potential difference needed to observe any Balmer series lines in the emission spectra will be

\frac{α}{10} V

, where

α =

______.

Answer: 121

Solution

Since the experiment is carried out at

T = 0

K, every hydrogen atom starts in the ground state (

n = 1

) before bombardment. The lowest-energy Balmer line corresponds to the

n = 3 \to n = 2

transition, so an electron must first be raised all the way from

n = 1

n = 3

for any Balmer line to appear. The bombarding electron must supply this excitation energy:

Δ E = 13.6 (1 - \frac{1}{3 ^{2}}) = 13.6 \times \frac{8}{9} \approx 12.09 eV

This energy is delivered by the accelerating potential,

e V = Δ E

, so

V \approx 12.1

= \frac{121}{10}

α = 121

JEE Main · 2024 · 29 Jan 2024 · Shift 2 · Integer answer

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JEE Main · 2024 · 29 Jan 2024 · Shift 2 · Modern Physics

Solution

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