The wavelength of the radiation emitted is… - JEE Main 2023 Physics PYQ

JEE Main 2023 — Physics Modern Physics

2023integermedium

The wavelength of the radiation emitted is ${\lambda }_{0}$ when an electron jumps from the second excited state to the first excited state of hydrogen atom. If the electron jumps from the third excited state to the second orbit of the hydrogen atom, the wavelength of the radiation emitted will be $\frac{20}{x}{\lambda }_{0}$ . The value of $x$ is________.

Official previous-year question

Held on 25 Jan 2023 · Verified 6 Jul 2026.

Did you get this right?

Solution

$_____n=4$

$_____n=3$

$_____n=2$

$_____n=1$

The wavelength of the light released when an electron jumps from higher energy state $({n}_{2})$ to lower energy state $({n}_{1})$ is $\frac{1}{\lambda }=R(\frac{1}{{n}_{1}^{2}}-\frac{1}{{n}_{2}^{2}})$ , here, $\lambda$ is wavelength, $R$ is Rydberg Constant.

When transition is from second excited state to first excited state,

$n=3\rightarrow n=2$

$\frac{1}{{\lambda }_{0}}=R(\frac{1}{{2}^{2}}-\frac{1}{{3}^{2}})...(1)$

When transition is from third excited state to second orbit

$n=4\rightarrow n=2$

$\frac{1}{(\frac{20}{x}{\lambda }_{0})}=R(\frac{1}{{2}^{2}}-\frac{1}{{4}^{2}})...(2)$

Dividing $(2)\mathrm{by}(1)$

$\Rightarrow \frac{x}{20}=\frac{\frac{1}{{2}^{2}}-\frac{1}{{4}^{2}}}{\frac{1}{{2}^{2}}-\frac{1}{{3}^{2}}}=\frac{\frac{1}{4}-\frac{1}{16}}{\frac{1}{4}-\frac{1}{9}}=\frac{\frac{3}{16}}{\frac{5}{36}}=\frac{27}{20}$

$\Rightarrow x=27$

Your note

JEE Main Modern Physics in other years

Modern Physics 2026 Modern Physics 2025 Modern Physics 2024 Modern Physics 2022 Modern Physics 2021 Modern Physics 2020 Modern Physics 2019 Modern Physics 2018 Modern Physics 2017 Modern Physics 2016 Modern Physics 2015 Modern Physics 2014

More JEE Main Modern Physics questions

An electron is travelling with a velocity $v$ in free space and when it enters a medium, its velocity is reduced by $20\%$. The de Broglie wavelength of electron in the medium is $\alpha\lambda_0$, where $\lambda_0$ is its de Broglie wavelength in free space. The value of $\alpha$ is _______.

2026easy

The maximum rated power of the LED is $2$ mW and it is used in the circuit with input voltage of $5$ V as shown in the figure below. The current through resistance $R_S$ is $0.5$ mA. The minimum value of the resistance of $R_S$, to ensure that the LED is not damaged is _______ k$\Omega$. ![JEE Main 2026 Physics, Semiconductors — question figure](https://prepforbharat.s3.ap-south-1.amazonaws.com/exam/615f0e999476412f48314daf/Physics/images/Semiconductors/69d8074d81239f6567c4f423/question_1__q_69d8074d81239f6567c4f423__cdn-question-pool.getmarks.app__06APRS1__q39_d1__cc54579e61_final_ppt_sync.png)

2026medium

Two $4$ bits binary numbers, $A = 1101$ and $B = 1010$ are given in the inputs of a logic circuit shown in figure below. The output $(Y)$ will be: ![JEE Main 2026 Physics, Semiconductors — question figure](https://prepforbharat.s3.ap-south-1.amazonaws.com/exam/615f0e999476412f48314daf/Physics/images/Semiconductors/69d8075381239f6567c4f46d/question_1__q_69d8075381239f6567c4f46d__cdn-question-pool.getmarks.app__04APRS1__q38_d1__175b657270_final_ppt_sync.png)

2026easy

Assuming the experimental mass of ${}^{12}_{6}C$ as $12\text{ u}$, the mass defect of ${}^{12}_{6}C$ atom is _______ $\text{MeV}/c^2$. (Mass of proton $= 1.00727\text{ u}$, mass of neutron $= 1.00866\text{ u}$, $1\text{ u} = 931.5\text{ MeV}/c^2$ and $c$ is the speed of the light in vacuum).

2026medium

A light wave described by $E=60\left[\sin \left(3 \times 10^{15}\right) t+\sin \left(12 \times 10^{15}\right) t\right]$ (in SI units) falls on a metal surface of work function 2.8 eV. The maximum kinetic energy of ejected photoelectron is (approximately) $\_\_\_\_$ eV. $\left(h=6.6 \times 10^{-34} \mathrm{~J}\right.$. s. and $\left.e=1.6 \times 10^{-19} \mathrm{C}\right)$

2026medium

View all Modern Physics questions