The nagative muon has charge equal to that of an electron but a mass that is 207 times as great. Consider hydrogen like atom consisting of a proton and a muon.
(a) What is the reduced mass of the atom?
(b) What is the ground-level energy (in eV)?
(c ) What is the wavelength of the radiation emitted in the transiton from the n=2 level to the n=1 level?

Answer

A, B, C

Explanation

(a) Reduced mass
`mu = (m_1m_2)/(m_1+M_2) = ((1837m_(e)(207m_e))/(1837m_e + 207m_e)`
`=186m_2`
`= 186xx9.1 xx10^(-31)`
`= 1.69xx10^(-28) kg.` (b) `E_n prop m`
Here, reduced mass is 186 times mass of
electron. Hence, ground state energy will also
be 186 times that of hydrogen atom.
`:. E_1 = 186(-13.6) eV`
`=- 2529.6 eV ~~-2.53 keV`
(c) `E_2 = 186(-3.4) eV =-632.4 eV`
`:. DeltaE_(21) = 1897.2 eV`
`:. lambda_(21) = (12375)/(DeltaE_(21) Å`
`= (12375)/(1897.2) Å`
=6.53 Å ~~0.653 nm.`