Physics Class 12 NCERT Solutions: Chapter 12 Atoms Part 3 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Bohr՚s Atomic Model

Q: 7. (A) Using the Bohr՚s model calculate the speed of the electron in a hydrogen atom in the levels. (B) Calculate the orbital period in each of these levels.

Let be the orbital speed of the electron in a hydrogen atom in the ground state level, . For charge (e) of an electron, is given by the relation,

Where,

Permittivity of free space

Planck՚s constant

For level , we can write the relation for the corresponding orbital speed as:

And, for , we can write the relation for the corresponding orbital speed as:

Hence, the speeds of the electron in a hydrogen atom in are , , respectively.

(B) Let be the orbital period of the electron when it is in level .

Orbital period is related to orbital speed as:

Where,

Radius of the orbit

Planck՚s constant

Charge on an electron

Permittivity of free space

Mass of an electron

For level , we can write the period as:

Where,

Radius of the electron in

And, for level , we can write the period as:

Where,

Radius of the electron in

Hence, the orbital period in each of these levels is , respectively.

Q: 8. The radius of the innermost electron orbit of a hydrogen atom is . What are the radii of the and orbits?

Answer:

The radius of the innermost orbit of a hydrogen atom .

Let be the radius of the orbit at . It is related to the radius of the innermost orbit as:

For , we can write the corresponding electron radius as:

Hence, the radii of an electron for and orbits are and respectively.

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