A mass spectrometer is used to determine the radius of the isotopes of certain e

Question

A mass spectrometer is used to determine the radius of the isotopes of certain elements. A proton (mass = 1.67 times 10^-27 kg) of charge q = 1.6 times 10^-19 C is projected to the spectrometer with an electric field E = 3.79 times 10^5 N/C and a magnetic field B = 0.50 T. (a) What is the velocity (selector) of the proton v_p? (b) Determine the radius of curvature of the path taken by the proton r_p. (c) If the particle projected is a deuteron (hydrogen isotope, mass of deuteron m_d = twice the mass of a proton = 2 times 1.6 times 10^-27 kg and the velocity of deuteron V_d = 5.36 times 10^5 m/s) instead of a proton, what is the radius of curvature of the deuteron r_d?

Explanation / Answer

as we know

E=vB

v=E/B=3.79*10^5/0.5=7.58*10^5m/s

b)radius=mv/qB=(1.67*10^-27 *7.58*10^5)/(1.6*10^-19*0.5)=15.8*10^-3 m

c)r=mv/qB

rd/rp=(mv)d/(mv)p

rd/(15.8*10^-3)=(2*mp*5.36*10^5)/(mp*7.58*10^5)

rd=22.345*10^-3 m

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