Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • A muon is an unstable elementary particle whose mass is &

A muon is an unstable elementary particle whose mass is 207 \mathrm{m}_{\mathrm{e}} and whose charge is either +e or -e . A negative muon \left(\mu^{\prime}\right) can be captured by a hydrogen nucleus (or proton) to form a muonic atom. Find the radius (in meter) of the first Bohr orbit of this atom - 

Option: 1

5 \times 10^{-13}


Option: 2

6.85 \times 10^{-13}


Option: 3

2.85 \times 10^{-13}


Option: 4

5.7 \times 10^{-13}


Answers (1)

best_answer

 

 

\begin{array}{l}{\text { Here } m=207 m_{e} \text { and } M=1836 m_{e} ; \text { so the reduced mass is }} \\ \\ {\mu=\frac{m M}{m+M}=\frac{\left(207 m_{e}\right)\left(1836 m_{e}\right)}{207 m_{e}+1836 m_{e}}=186 m_{e}} \\ \\ {\text { According to equation } \lambda=h / p, \text { the orbit radius }} \\ \\ {\text { corresponding to } n=1 \text { is } r_{1}=\frac{h^{2} \varepsilon_{0}}{\pi m_{e} e^{2}}=5.29 \times 10^{-11} \mathrm{m}}\end{array}

\begin{array}{l}{\text { Hence, the radius } r^{\prime} \text { that corresponds to the reduced mass } \mu} \\ {\text { is }} \\ {\qquad r_{1}^{\prime}=\left(\frac{m}{\mu}\right) r_{1}=\left(\frac{m_{e}}{186 m_{e}}\right) r_{1}=2.85 \times 10^{-13} \mathrm{m}}\end{array}

Posted by

Kuldeep Maurya

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions