The Total solution for NCERT class 6-12
Obtain the first BohrтАЩs radiusand the ground state energy of a┬аmuonic┬аhydrogen atom┬а[i.e.,an atom in which a negatively charged muon (╬╝тИТ) of mass about 207me┬аorbitsaround a proton].
Mass of a negatively charged muon,┬а
According to BohrтАЩs model,
Let┬аr╬╝┬аbethe radius of┬аmuonic hydrogen atom.
At equilibrium, we can write therelation as:
Hence, the value of the firstBohr radius of a┬аmuonic hydrogen atom┬аis
2.56 ├Ч 10тИТ13┬аm.
We have,
Ee= тИТ 13.6eV
Take the ratio of these energiesas:
Hence, the ground state energy ofa┬аmuonic hydrogen atom┬аis тИТ2.81 keV.