if muonic hydrogen atom is an atom in which a negatively charged muon `(mu)` of mass about `207m_e` revolves around a proton, then first bohr radius of this atom is `(r_e=0.53xx10^(-10)m)`

Options

A. `2.56xx10^(-10)m`
B. `2.56xx10^(-11)m`
C. `2.56xx10^(-12)m`
D. `2.56xx10^(-13)m`

Answer

D

Explanation

According to bohr's atomic model.
`rprop(1)/(m)rArr(r_mu)/(r_e)=(m_e)/(m_mu)`......(i)
Here, `r_e=0.53xx10^(-10)m,m_mu=207m_e`
`therefore r_mu=(m_e)/(207m_e)xx0.53xx10^(-10)`(using(i)
`=2.56xx10^(-13)m`.