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Question 73 of 127

Q.Arrange electron (e), proton (p) and deutron

(d) in the increasing order of their specific charge :
(a) e, p, d
(b) d, p, e
(c) p, e, d
(d) d, e, p
Puducherry TnboardTamil Nadu HSC (DGE) Board 2017MCQ· 1mImportance★★★★★
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Specific charge q/mq/m is largest for the lightest particle (electron) and smallest for the heaviest (deuteron), giving the increasing order deuteron, proton, electron.

Specific charge (charge-to-mass ratio) is defined as qm\dfrac{q}{m}, and it is exactly this ratio that a Bainbridge-type mass spectrometer or a Thomson e/me/m apparatus measures via the radius of circular deflection in a magnetic field (r=mvqBr = \dfrac{mv}{qB}, so qm=vrB\dfrac{q}{m}=\dfrac{v}{rB}).

For the electron, the charge magnitude is the elementary charge e=1.6×10−19e = 1.6\times10^{-19} C, and its mass is extremely small, me=9.11×10−31m_e = 9.11\times10^{-31} kg, giving a specific charge eme≈1.76×1011\dfrac{e}{m_e}\approx 1.76\times10^{11} C/kg — by far the largest of the three, because the electron is thousands of times lighter than the proton for the same magnitude of charge.

For the proton, the charge is also +e+e, but the mass is mp=1.67×10−27m_p = 1.67\times10^{-27} kg (about 1836 times the electron's mass), giving emp≈9.58×107\dfrac{e}{m_p}\approx 9.58\times10^{7} C/kg.

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