Class 12 Physics
CBSE and UP Board
Dual Nature of Radiation and Matter
Chapter-11 Exercise 11.22
NCERT Solutions for Class 12 Physics Chapter 11 Question-22
Additional Exercise
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
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Potential of an anode, V = 100 V
Magnetic field experienced by the electrons, B = 2.83 x 10-4 T
Radius of the circular orbit r = 12.0 cm = 12.0 x 10-2 m
Mass of each electron = m and
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 mv² = eV
v²= 2eV/m————- Eq-1
It is the magnetic field, due to its bending nature, that provides the centripetal force (F = mv²/r) Centripetal force = Magnetic force
mv²/r = evB
eB = mv/r
v = eBr/m ——Eq-2
Putting the value of v in equation (1), we get:
2eV/m = e²B²r²/m²
e/m = 2V/B²r²
= 2 x 100 / (2.83 x 10-4 ) x (12.0 x 10-2) = 1.73 x 10¹¹Ckg-1
Therefore, the specific charge ratio (e/m) is 1.73 x 10¹¹ Ckg-1.