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Question
Calculate the momentum of the electrons accelerated through a potential difference of 56 V.
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Solution
Potential difference, V = 56 V
Planck’s constant, h = 6.6 × 10−34 Js
Mass of an electron, m = 9.1 × 10−31 kg
Charge on an electron, e = 1.6 × 10−19 C
At equilibrium, the kinetic energy of each electron is equal to the accelerating potential, i.e., we can write the relation for velocity (v) of each electron as:
`1/2 "mv"^2 = "eV"`
`"v"^2 = (2"eV")/"m"`
∴ v = `sqrt((2xx1.6xx10^(-19) xx 56)/(9.1 xx 10^(-31)))`
= `sqrt(19.69 xx 10^12)`
= 4.44 × 106 m/s
The momentum of each accelerated electron is given as:
p = mv
= 9.1 × 10−31 × 4.44 × 106
= 4.04 × 10−24 kg m s−1
Therefore, the momentum of each electron is 4.04 × 10−24 kg m s−1.
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