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NCERT Class XII Chapter
Dual Nature of Radiation and Matter
Questions With Solutions

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Question : 22
Total: 37
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. Determine e/m from the data.
Solution:  
Here V = 100 V, r = 12 cm = 12 × 10–2 m, B = 2.83 × 10–4 T
The gain in kinetic energy of an electron when accelerated through V volts is
1
2
mv2 = eV or v2 =
2eV
m
As the magnetic field provides centripetal force to the electron, therefore,
evB =
mv2
r
 or v =
eBr
m
v2 =
e2B2r2
m2
∴
2eV
m
 =
e2B2r2
m2
Specific Charge ,
e
m
 =
2V
B2r2
 =
2×100
(2.83×10−4)2×(12×10−12)2
= 1.73 × 1011CKg−1
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