Physics Class 12 NCERT Solutions: Chapter 12 Atoms Part 4 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Rydberg Equation

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

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