Physics Class 12 NCERT Solutions: Chapter 12 Atoms Part 4

Get top class preparation for CBSE right from your home: fully solved questions with step-by-step explanation- practice your way to success.

Rydberg Equation

Rydberg Equation

Loading Image

Q: 9. A electron beam is used to bombard gaseous hydrogen at room temperature. What series of wavelengths will be emitted?

Answer:

It is given that the energy of the electron beam used to bombard gaseous hydrogen at room temperature is . Also, the energy of the gaseous hydrogen in its ground state at room temperature is .

When gaseous hydrogen is bombarded with an electron beam, the energy of the gaseous hydrogen becomes

Orbital energy is related to orbit level (n) as:

For ,

This energy is approximately equal to the energy of gaseous hydrogen. It can be concluded that the electron has jumped from to level.

During its de-excitation, the electrons can jump from to directly, which forms a line of the Lyman series of the hydrogen spectrum.

We have the relation for wave number for Lyman series as:

Where,

Rydberg constant

Wavelength of radiation emitted by the transition of the electron

For, we can obtain as:

If the electron jumps from to, then the wavelength of the radiation is given as:

If the transition takes place from to, then the wavelength of the radiation is given as:

This radiation corresponds to the Balmer series of the hydrogen spectrum.

Hence, in Lyman series, two wavelengths i.e., and are emitted. And in the Balmer series, one wavelength i.e., is emitted.

Q: 10. In accordance with the Bohr’s model, find the quantum number that characterises the earth’s revolution around the sun in an orbit of radius with orbital speed. (Mass of earth.

Answer:

Radius of the orbit of the Earth around the Sun,

Orbital speed of the Earth,

Mass of the Earth,

According to Bohr’s model, angular momentum is quantized and given as:

Where,

Planck’s constant

Quantum number

Hence, the quanta number that characterizes the Earth’ revolution is