Question

Chlorine has two stable isotopes, ³⁵Cl and ³⁷Cl. Chlorine gas which consists of singly ionized ions is to be separated into its isotopic components using a mass spectrometer. The magnetic field strength in the spectrometer is 1.1 T. What is the minimum value of the potential difference through which these ions must be accelerated so that the separation between them, after they complete their semicircular path, is 1.4 cm?
MV

Answer 1

considering energy conservation

0.5 m v^2 = q V

v = sqrt ( 2 qV / m)

now, radius exhibit by the charge

r = mv / qB = m sqrt ( 2 qV / m) / (qB)

r = sqrt ( 2 m V / qB^2)

now, for 35 Cl

r1 = sqrt ( 2 * 35* V / 1.6* 10^-19* 1.1^2)

for 37 Cl

r2 = sqrt ( 2 * 37* V / 1.6* 10^-19* 1.1^2)

given that

r2 - r1 = 0.014 /2

sqrt ( 70 V / 1.6* 10^-19* 1.1^2) - sqrt ( 74 V / 1.6* 10^-19* 1.1^2) = 0.007

V = 0.1022 MV

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