An electron from various… - JEE Main 2018 Physics PYQ

JEE Main 2018 — Physics Modern Physics

2018mcqhard

An electron from various excited states of hydrogen atom emit radiation to come to the ground state. Let ${\lambda }_{n}, {\lambda }_{g}$ be the de Broglie wavelength of the electron in the ${n}^{th}$ state and the ground state respectively. Let ${\wedge }_{n}$ be the wavelength of the emitted photon in the transition from the ${n}^{th}$ state to the ground state. For large n, (A, B are constants)

Official previous-year question

Held on 8 Apr 2018 · Verified 6 Jul 2026.

Options

A
${\wedge }_{n}^{2}\approx \lambda$
B
${\wedge }_{n}\approx A+\frac{B}{{\lambda }_{n}^{2}}$
C
${\wedge }_{n}\approx A+B{\lambda }_{n}$
D
${\wedge }_{n}^{2}\approx A+B{\lambda }_{n}^{2}$

Did you get this right?

Solution

$2\pi r=n{⋋}_{n}$

${⋋}_{n}=\frac{2\pi r}{n}$

$\therefore r={r}_{o}{n}^{2}$

${⋋}_{n}=\frac{2\pi }{n} {r}_{o}{n}^{2}=n(2\pi {r}_{o})\ldots ..(i)$

$\frac{1}{{\wedge }_{n}}=R{\frac{1}{{1}^{2}}-\frac{1}{{n}^{2}}}$

${\wedge }_{n}=\frac{1}{R}{1+\frac{1}{{n}^{2}-1}}$

${\wedge }_{n}=\frac{1}{R}{1+\frac{1}{{n}^{2}}}\ldots \ldots \ldots ..(\mathrm{ii})$

from $(i)$ and $(\mathrm{ii})$

${\wedge }_{n}=\frac{1}{R}{1+\frac{4{n}^{2}{r}_{o}^{2}}{{⋋}_{n}^{2}}}=A+\frac{B}{{⋋}_{n}^{2}}$

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Options

${\wedge }_{n}^{2}\approx \lambda$

${\wedge }_{n}\approx A+\frac{B}{{\lambda }_{n}^{2}}$

${\wedge }_{n}\approx A+B{\lambda }_{n}$

${\wedge }_{n}^{2}\approx A+B{\lambda }_{n}^{2}$

Solution

$2\pi r=n{⋋}_{n}$

${⋋}_{n}=\frac{2\pi r}{n}$

$\therefore r={r}_{o}{n}^{2}$

${⋋}_{n}=\frac{2\pi }{n} {r}_{o}{n}^{2}=n(2\pi {r}_{o})\ldots ..(i)$

$\frac{1}{{\wedge }_{n}}=R{\frac{1}{{1}^{2}}-\frac{1}{{n}^{2}}}$

${\wedge }_{n}=\frac{1}{R}{1+\frac{1}{{n}^{2}-1}}$

${\wedge }_{n}=\frac{1}{R}{1+\frac{1}{{n}^{2}}}\ldots \ldots \ldots ..(\mathrm{ii})$

from $(i)$ and $(\mathrm{ii})$

${\wedge }_{n}=\frac{1}{R}{1+\frac{4{n}^{2}{r}_{o}^{2}}{{⋋}_{n}^{2}}}=A+\frac{B}{{⋋}_{n}^{2}}$

Options

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Solution

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Options

Did you get this right?

Solution

Your note

JEE Main Modern Physics in other years

More JEE Main Modern Physics questions

Other Physics topics for JEE Main

Mechanics

Electromagnetism

Optics

Thermodynamics

Waves & Oscillations

Keep practicing Modern Physics