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Muon ( \mu ^{-}) is a negatively charged ( |q| = |e| ) particle with a mass m_{\mu } =200 m_{e }, where m_{e} 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.

(A) Radius of the muonic orbit is 200 times smaller than that of the electron.

(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.

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

  • Option 1)

    (A), (B), (D)

  • Option 2)

    (A), (C), (D)

  • Option 3)

    (B), (D)

  • Option 4)

    (C), (D)

 

Answers (2)

best_answer

As we learnt

Radius of nth orbital -

r_{n}= \frac{\epsilon _{0}n^{2}h^{2}}{\pi mZe^{2}}

 

- wherein

r_{n}\alpha \: \frac{n^{2}}{Z}

\frac{\epsilon_{0}h^{2}}{\pi me^{2}}= 0.529A^{\circ}

 

 and

 

Energy of electron in nth orbit -

E= -\left ( \frac{me^{4}}{8\epsilon _{0}^{2}h^{2}} \right )\frac{z^{2}}{n^{2}}

 

- wherein

E\alpha \frac{z^{2}}{n^{2}} \\\frac{me^{4}}{8\epsilon_{0}^{2}h^{2}}= 13.6ev

 

 R=\frac{\epsilon _{0}n^{2}h^{2}}{\Pi mze^{2}}.,\: \: E=\frac{mz^{2}e^{4}}{8\epsilon _{0}^{2}n^{2}h^{2}}

m{}'=200m_{e}

R{}'=\frac{R}{200};\: \: {E}'=200E

p{}'=200\phi


Option 1)

(A), (B), (D)

Option 2)

(A), (C), (D)

Option 3)

(B), (D)

Option 4)

(C), (D)

Posted by

Avinash

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