Physics Class 12 NCERT Solutions: Chapter 11 Dual Nature of Radiation and Matter Part 10

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Calculation of ratio e/m

Calculation of Ratio E/M

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Q: 22. An electron gun with its collector at a potential of fires out electrons in a spherical bulb containing hydrogen gas at low pressure of. A magnetic field of curves the path of the electrons in a circular orbit of radius. (The path can be viewed because the gas ions in the path focus the beam by attracting electrons, and emitting light by electron capture; this method is known as the ‘fine beam tube’ method. Determine e/m from the data.


Potential of an anode,

Magnetic field experienced by the electrons,

Radius of the circular orbit

Mass of each electron

Charge on each electron

Velocity of each electron

The energy of each electron is equal to its kinetic energy, i.e.,

It is the magnetic field, due to its bending nature, that provides the centripetal force for the beam. Hence, we can write:

Centripetal force Magnetic force

Putting the value of v in equation (1), we get:

Therefore, the specific charge ratio is.

Q: 23. (A) An X-ray tube produces a continuous spectrum of radiation with its short wavelength end at .What is the maximum energy of a photon in the radiation?

(B) From your answer to (a), guess what order of accelerating voltage (for electrons) is required in such a tube?


(A) Wavelength produced by an X-ray tube,

Planck’s constant,

Speed of light,

The maximum energy of a photon is given as:

Therefore, the maximum energy of an X-ray photon is.

(B) Accelerating voltage provides energy to the electrons for producing X-rays. To get an X-ray of, the incident electrons must possess at least of kinetic electric energy. Hence, an accelerating voltage of the order of is required for producing X-rays.

Q: 24. In an accelerator experiment on high-energy collisions of electrons with positrons, a certain event is interpreted as annihilation of an electron-positron pair of total energy into tworays of equal energy. What is the wavelength associated with each Y-ray?


Total energy of two -rays:

Hence, the energy of each -ray:

Planck’s constant,

Speed of light,

Energy is related to wavelength as:

Therefore, the wavelength associated with each is m