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# Solution for An Electron Gun with Its Collector at a Potential of 100 V Fires Out Electrons in a Spherical Bulb Containing Hydrogen Gas at Low Pressure (∼10−2 Mm of Hg) Determine E/M From the Data. - CBSE (Science) Class 12 - Physics

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ConceptPhotoelectric Effect and Wave Theory of Light

#### Question

An electron gun with its collector at a potential of 100 V fires out electrons in a spherical bulb containing hydrogen gas at low pressure (∼10−2 mm of Hg). A magnetic field of 2.83 × 10−4 T curves the path of the electrons in a circular orbit of radius 12.0 cm. (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.

#### Solution

Potential of an anode, = 100 V

Magnetic field experienced by the electrons, B = 2.83 × 10−4 T

Radius of the circular orbit r = 12.0 cm = 12.0 × 10−2 m

Mass of each electron = m

Charge on each electron = e

Velocity of each electron = v

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

1/2 mv^2 = eV

v^2 = (2eV)/m    ...(1)

It is the magnetic field, due to its bending nature, that provides the centripetal force

(F = mv^2/r)  for the beam. Hence, we can write:

Centripetal force = Magnetic force

mv^2/r = evB

eB = mv/r

v = (eBr)/m   ...(2)

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

"2eV"/m = (e^2B^2r^2)/m^2

e/m = "2V"/(B^2r^2)

= (2xx100)/((2.83xx 10^(-4))^2 xx (12 xx 10^(-2))^2)= 1.73 xx 10^11 C kg^(-1)

Therefore, the specific charge ratio (e/m) is 1.73 xx 10^11 C Kg^(-1)

Is there an error in this question or solution?

#### APPEARS IN

NCERT Solution for Physics Textbook for Class 12 (2013 to Current)
Chapter 11: Dual Nature of Radiation and Matter
Q: 22 | Page no. 409
Solution An Electron Gun with Its Collector at a Potential of 100 V Fires Out Electrons in a Spherical Bulb Containing Hydrogen Gas at Low Pressure (∼10−2 Mm of Hg) Determine E/M From the Data. Concept: Photoelectric Effect and Wave Theory of Light.
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