4· /1 points TiplerG 26·P.038. My NotesAsk Your Teacher Chlorine has two stable

Question

4· /1 points TiplerG 26·P.038. My NotesAsk Your Teacher Chlorine has two stable isotopes, 35Cl and 37ci. 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 1.6 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 1.2 cm? MV eBook Submit Answer Save Progress Practice Another Version

Explanation / Answer

we know radius of circular path, r = m*v/(B*q)

= sqrt(2*m*KE)/(B*q)

= sqrt(2*m*q*V)/(B*q)

= sqrt(2*m*V/(B^2*q))

so, diameter, d = 2*sqrt(2*m*V/(B^2*q))

d2 - d1 = 2*sqrt(2*m*V/(B^2*q)) - 2*sqrt(2*m*V/(B^2*q))

1.2*10^-2 = 2*sqrt(2*V/(B^2*q))*(sqrt(m2) - sqrt(m1))

1.2*10^-2 = s*sqrt(2*V/(1.6^2*1.6*10^-19))*(sqrt(37*1.67*10^-27) - sqrt(35*1.67*10^-27) )

==> V = 0.656*10^6 V

= 0.656 MV

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