Physics Class 12 NCERT Solutions: Chapter 12 Atoms Part 3

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Bohr's atomic model

Bohr's Atomic Model

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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.