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  4. A monochromatic radiation of wavelength λ is incident on a sample containing He +. As a result the Helium sample starts radiating. A part of this radiation is allowed to pass through a sample of atomic hydrogen gas in ground state. It is noticed that the hydrogen sample has started emitting electrons whose maximum Kinetic Energy is 37.4 eV. (he =12400 eV mathringA ) Then λ is :

Q. A monochromatic radiation of wavelength $\lambda$ is incident on a sample containing $He ^{+}$. As a result the Helium sample starts radiating. A part of this radiation is allowed to pass through a sample of atomic hydrogen gas in ground state. It is noticed that the hydrogen sample has started emitting electrons whose maximum Kinetic Energy is $37.4\, eV$. (he $=12400\, eV \,\mathring{A}$ ) Then $\lambda$ is :

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Solution:

Maximum energy of radiation incident on $H$-sample $=K E_{\max }$ of electron $+13.6\, eV =51\, eV$ this energy corresponds to the transition
$n=4 \rightarrow n=1$ in Helium
For electrons of the He to get excited to $n=4$
$\lambda=\frac{12431}{51}=243\,\mathring{A}$

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2. 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.
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(D) The momentum of the muon in the $n^{th}$ orbit is $200 $ times more than that of the electron.

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