Physics Class 12 NCERT Solutions: Chapter 12 Atoms Part 8 (For CBSE, ICSE, IAS, NET, NRA 2022)

Get top class preparation for CBSE/Class-12 right from your home: get questions, notes, tests, video lectures and more- for all subjects of CBSE/Class-12.

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 .

Developed by: