(D) For the transition from $2E$ to $E$:$\Delta E_1 = 2E - E = E = \frac{hc}{\lambda} \implies E = \frac{hc}{\lambda}$ (Equation $1$)For the transitio

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(D) For the transition from $2E$ to $E$:$\Delta E_1 = 2E - E = E = \frac{hc}{\lambda} \implies E = \frac{hc}{\lambda}$ (Equation $1$)For the transition from $\frac{4E}{3}$ to $E$:$\Delta E_2 = \frac{4E}{3} - E = \frac{E}{3} = \frac{hc}{\lambda'}$ (Equation $2$)Substituting the value of $E$ from Equation $1$ into Equation $2$:$\frac{1}{3} \left( \frac{hc}{\lambda} \right) = \frac{hc}{\lambda'}$$\frac{1}{3\lambda} = \frac{1}{\lambda'} \implies \lambda' = 3\lambda$Therefore,the correct option is $(D)$.

Class 12 Physics Atoms Electron Energy and Electron Energy Levels in Hydrogen Atom

Medium

The following diagram indicates the energy levels of a certain atom. When the system moves from the $2E$ level to the $E$ level,a photon of wavelength $\lambda$ is emitted. The wavelength of the photon produced during its transition from the $\frac{4E}{3}$ level to the $E$ level is

A
$\lambda / 3$
B
$3\lambda / 4$
C
$4\lambda / 3$
D
$3\lambda$

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Electron Energy and Electron Energy Levels in Hydrogen Atom

The minimum energy required by a hydrogen atom in the ground state to emit radiation in the Balmer series is nearly: (in $eV$)

DifficultJEE MAIN 2024

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Three energy levels of a hydrogen atom and the corresponding wavelengths of the emitted radiation due to different electron transitions are as shown. Then,

MediumKCET 2023

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The energy of a hydrogen atom in its ground state is $-13.6 \, eV$. The energy of the level corresponding to the quantum number $n = 5$ is ...... $eV$.

Easy

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In the third orbit of a hydrogen atom,the energy of an electron is $E$. In the fifth orbit of a helium ion $(Z=2)$,the energy of an electron will be:

EasyMHT CET 2024

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The total energy of an electron in the first excited state of the hydrogen atom is about $-3.4 \; eV.$
$(a)$ What is the kinetic energy of the electron in this state?
$(b)$ What is the potential energy of the electron in this state?
$(c)$ Which of the answers above would change if the choice of the zero of potential energy is changed?

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The following diagram indicates the energy levels of a certain atom. When the system moves from the $2E$ level to the $E$ level,a photon of wavelength $\lambda$ is emitted. The wavelength of the photon produced during its transition from the $\frac{4E}{3}$ level to the $E$ level is

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The minimum energy required by a hydrogen atom in the ground state to emit radiation in the Balmer series is nearly: (in $eV$)

Three energy levels of a hydrogen atom and the corresponding wavelengths of the emitted radiation due to different electron transitions are as shown. Then,

The energy of a hydrogen atom in its ground state is $-13.6 \, eV$. The energy of the level corresponding to the quantum number $n = 5$ is ...... $eV$.

In the third orbit of a hydrogen atom,the energy of an electron is $E$. In the fifth orbit of a helium ion $(Z=2)$,the energy of an electron will be:

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