The Total solution for NCERT class 6-12
Obtain the first Bohr’s radiusand the ground state energy of a muonic hydrogen atom [i.e.,an atom in which a negatively charged muon (μ−) of mass about 207me orbitsaround a proton].
Mass of a negatively charged muon,
According to Bohr’s model,
Let rμ bethe radius of muonic hydrogen atom.
At equilibrium, we can write therelation as:
Hence, the value of the firstBohr radius of a muonic hydrogen atom is
2.56 × 10−13 m.
We have,
Ee= − 13.6eV
Take the ratio of these energiesas:
Hence, the ground state energy ofa muonic hydrogen atom is −2.81 keV.