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  • The radius of the hydrogen atom in its ground state is . The radius of a muonic hydrogen atom in which the electron is replaced by a

The radius of the hydrogen atom in its ground state is \mathrm{a}_0. The radius of a muonic hydrogen atom in which the electron is replaced by an identically charged muon with mass 207 times that of an electron, is \mathrm{a}_\mu equal to:

 

Option: 1

107 \mathrm{a}_0


Option: 2

\frac{\mathrm{a}_0}{207}


Option: 3

\frac{\mathrm{a}_0}{\sqrt{207}}


Option: 4

\mathrm{a}_0 \sqrt{207}


Answers (1)

best_answer

a_0=\frac{h^2 \varepsilon_0}{\pi m e^2} \ \ \ \ \ \ \ \ \ \dots (i)
 

\mathrm{a}_\mu=\frac{\mathrm{h}^2 \varepsilon_0}{\pi(207 \mathrm{~m}) \mathrm{e}^2} \ \ \ \ \ \ \ \ \ \dots (ii)
Dividing (ii) by (i),

we get, 

\frac{\mathrm{a}_\mu}{\mathrm{a}_0}=\frac{1}{207} \text{ or } \mathrm{a}_\mu=\frac{\mathrm{a}_0}{207}

Posted by

shivangi.shekhar

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