Q. The photon radiated from hydrogen corresponding to $2^{\text {nd }}$ line of Lyman series is absorbed by a hydrogen like atom ' $X$ ' in $2^{\text {nd }}$ excited state. As a result the hydrogen like atom ' $X$ makes a transition to $n^{\text {th }}$ orbit. Then,

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A

$X= He ^{+}, n=4$

B

$X= Li ^{++}, n=6$

C

$X= He ^{+}, n=6$

D

$X=Li ^{+4}, n=9$

Solution:

Energy of $n^{\text {th }}$ sate in Hydrogen is same as energy of $3 n^{\text {th }}$ state in $Li ^{++}$.
$\Rightarrow$ For $3 \rightarrow 1$ transition in $H$ would it give same energy as the $3 \times 3 \rightarrow 1 \times 3$ transition in $Li ^{++}$.

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4. Muon $ (\mu^{-})$ is a negatively charged $(|q | = |e|$ particle with a mass $m_{\mu} = 200$ me, where me is the mass of the electron and e is the electronic charge. If $\mu$- is bound to a proton to form a hydrogen like atom, identify the correct statements.
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(B) The speed of the $\mu^{-}$ in the $n^{th}$ orbit is $\frac{1}{200}$ times that of the electron in the $n^{th}$ orbit.
(C) The ionization energy of muonic atom is $200$ times more than that of an hydrogen atom.
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