1
IAT (IISER) 2020
MCQ (Single Correct Answer)
+4
-1

An electron of mass $m_e$ has a speed $u_n$ in the $n^{\text {th }}$ Bohr orbit of a hydrogen atom. The normalized speed $V_n$ is given as $V_n=u_n / c=1 / 685$ and the mass of the electron in the units of energy is given as $M_e=m_e c^2=0.51 \times 10^6 \mathrm{eV}$, where $c$ is the velocity of light in a vacuum. It is given that $\frac{e^2}{2 \epsilon_0 h c}=1 / 137$. The Planck's constant h is given as $4.13 \times 10^{-15} \mathrm{eV}-\mathrm{sec}$. The electron makes a transition from $n^{\text {th }}$ orbit to the ground state of the atom. What is the frequency of the emitted photon?

A
$3.29 \times 10^{15} \mathrm{~Hz}$
B
$2.47 \times 10^{15} \mathrm{~Hz}$
C
$2.93 \times 10^{15} \mathrm{~Hz}$
D
$3.16 \times 10^{15} \mathrm{~Hz}$
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