11.22 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 ( 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.
11.22 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 ( 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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1 Answer
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11.22 Potential, V = 100 V
Magnetic field experienced by electron, B = 2.83 T
Radius of the circular orbit, r = 12.0 cm = 12 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.
m =
…….(1)
Since centripetal force ( = Magnetic force (evB), we can write
= ………………(2)
Equating equations (1) and (2) we get
= = = 1.734 C/kg
Therefore, the specific charge ratio (e/m) is 1.734 C/k
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Based on theory
z² × (13.6) (1 - ¼) = 3 × (13.6)
z = 2 . (i)
h/√2mk? = (1/2.3) × h/√2mk?
=> k? = (2.3)²k? = 5.25k? (ii)
Now, k? = E? - Φ
k? = E? - Φ = z²E? - Φ
∴ k? /k? = (10.2 - Φ)/ (4 × 10.2 - Φ) = 1/5.25
=> Φ = 3eV
- (i)
- (ii)
from (i) & (ii)
ev
hu = hu0 + K.E
Cases u = 2u0
h2u0 = hu0 + K.E1
K.E1 = hu0
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Now, cases 2
h 5u0 = hu0 + k.E2
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v2 =
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This is a Short Answer Type Questions as classified in NCERT Exemplar
Sol:
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