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Physics Class 12 NCERT Solutions: Chapter 12 Atoms Part 4
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 .
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