(A) The energy of an electron in the $n$-th orbit of a hydrogen atom is given by $E_n = -\frac{13.6 \ eV}{n^2}$.For the ground state $(n=1)$,$E_1 = -1

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(A) The energy of an electron in the $n$-th orbit of a hydrogen atom is given by $E_n = -\frac{13.6 \ eV}{n^2}$.For the ground state $(n=1)$,$E_1 = -13.6 \ eV$.For the second orbit $(n=2)$,$E_2 = -\frac{13.6}{2^2} = -3.4 \ eV$.The energy of the emitted photon during the transition from $n=2$ to $n=1$ is $\Delta E = E_2 - E_1 = -3.4 \ eV - (-13.6 \ eV) = 10.2 \ eV$.The frequency $\nu$ is given by $\Delta E = h\nu$,so $\nu = \frac{\Delta E}{h}$.Substituting the given values: $\nu = \frac{10.2 \ eV}{4 \times 10^{-15} \ eV \cdot s} = 2.55 \times 10^{15} \ Hz$.

Class 12 Physics Atoms Bohr's Model of Hydrogen Atom

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The frequency of light emitted,when the electron makes a transition from the level of principal quantum number $n=2$ to the level with $n=1$ is (Take,the ionization energy of hydrogen to be $13.6 \ eV$ and $h \simeq 4 \times 10^{-15} \ eV \cdot s$)

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A
$2.55 \times 10^{15} \ Hz$
B
$1.7 \times 10^{15} \ Hz$
C
$3.4 \times 10^{15} \ Hz$
D
$5.1 \times 10^{15} \ Hz$

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The frequency of light emitted,when the electron makes a transition from the level of principal quantum number $n=2$ to the level with $n=1$ is (Take,the ionization energy of hydrogen to be $13.6 \ eV$ and $h \simeq 4 \times 10^{-15} \ eV \cdot s$)

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In a hypothetical system,a particle of mass $m$ and charge $-3q$ is moving around a very heavy particle having charge $q$. Assuming Bohr's model to be true for this system,the orbital velocity of mass $m$ when it is nearest to the heavy particle is:

An electron makes a transition from orbit $n = 4$ to the orbit $n = 2$ of a hydrogen atom. The wave number of the emitted radiations ($R =$ Rydberg's constant) will be

The period of revolution of an electron in the ground state of a hydrogen atom is $T$. The period of revolution of the electron in the first excited state is

Assuming the atom is in the ground state, the expression for the magnetic field at the nucleus in a hydrogen atom due to the circular motion of the electron is [$\mu_0 =$ permeability of free space, $m =$ mass of electron, $\epsilon_0 =$ permittivity of free space, $h =$ Planck's constant].

The frequency of the light emitted when an electron transitions from the $n=4$ to $n=2$ level in a hydrogen atom is $\frac{3}{7}$ times the frequency of a transition in a $Li^{2+}$ ion. Which transition in the $Li^{2+}$ ion corresponds to this?

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