Physics Class 12 NCERT Solutions: Chapter 12 Atoms Part 8

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Energy levels formula

Energy Levels Formula

Q: 17. Obtain the first Bohr’s radius and the ground state energy of a muonic hydrogen atom [i.e., an atom in which a negatively charged muon of mass about 207me orbits around a proton].

Answer:

Mass of a negatively charged muon,

According to Bohr’s model,

Bohr radius,

And, energy of a ground state electronic hydrogen atom, .

Also, energy of a ground state muonic hydrogen atom, .

We have the value of the first Bohr orbit,

Let be the radius of muonic hydrogen atom.

At equilibrium, we can write the relation as:

Hence, the value of the first Bohr radius of a muonic hydrogen atom is .

We have,

Take the ratio of these energies as:

Hence, the ground state energy of a muonic hydrogen atom is.

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