Physics Class 12 NCERT Solutions: Chapter 11 Dual Nature of Radiation and Matter Part 16

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De - Broglie wavelength

De - Broglie Wavelength

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Q: 34. The wavelength of a probe is roughly a measure of the size of a structure that it can probe in some detail. The quark structure of protons and neutrons appears at the minute length-scale of or less. This structure was first probed in early using high energy electron beams produced by a linear accelerator at Stanford, USA. Guess what might have been the order of energy of these electron beams. (Rest mass energy of electron.)

Answer:

Wavelength of a proton or a neutron,

Rest mass energy of an electron:

Planck’s constant,

Speed of light,

The momentum of a proton or a neutron is given as:

The relativistic relation for energy (E) is given as:

Thus, the electron energy emitted from the accelerator at Stanford, USA might be of the order of.

Q: 35. Find the typical de Broglie wavelength associated with a He atom in helium gas at room temperature and pressure; and compare it with the mean separation between two atoms under these conditions.

Answer:

De Broglie wavelength associated with atom

Room temperature,

Atmospheric pressure,

Atomic weight of a He atom

Avogadro’s number,

Boltzmann constant,

Average energy of a gas at temperature T, is given as:

De Broglie wavelength is given by the relation:

Where,

Mass of a He atom

We have the ideal gas formula:

Where,

Volume of the gas

Number of moles of the gas

Mean separation between two atoms of the gas is given by the relation:

Hence, the mean separation between the atoms is much greater than the de Broglie wavelength.