Suppose the electric field between the plates P and P\' in the mass spectrometer

Question

Suppose the electric field between the plates P and P' in the mass spectrometer in following figure is 1.90×104 V/m and the magnetic field in both regions is 0.696 T .(Figure 1)

(a) If the source contains the three isotopes of krypton, 82Kr,84Kr, and 86Kr, and the ions are singly charged, find the distance between the two adjaicent lines formed by the three isotopes on the photographic plate. Assume the atomic masses of the isotopes (in atomic mass units) are equal to their mass numbers, 82, 84, and 86. (One atomic mass unit = 1u = 1.66×10?27 kg.)

Explanation / Answer

we know,
radius of orbit of charged particles, r = m*v/(B*q)

= P/(B*q)

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

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

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

from the given data,

m1 = 82*u = 82*1.66*10^-27 = 1.36*10^-25 kg

m2 = 84*u = 84*1.66*10^-27 = 1.394*10^-25 kg

m3 = 86*u = 86*1.66*10^-27 = 1.428*10^-25 kg

so, R1 = sqrt(2*m1*delta_V/q)/B

= sqrt(2*1.36*10^-25*1.9*10^4/(1.6*10^-19))/0.696

= 0.2582 m

R2 = sqrt(2*m2*delta_V/q)/B

= sqrt(2*1.394*10^-25*1.9*10^4/(1.6*10^-19))/0.696

= 0.2614 m

R3 = sqrt(2*m3*delta_V/q)/B

= sqrt(2*1.428*10^-25*1.9*10^4/(1.6*10^-19))/0.696

= 0.2646 m

distance between 84Kr and 82Kr = 2*(R2 - R1)

= 2*(0.2614 - 0.2582)

= 0.0064 m or 6.4 mm <<<<<<<<---------Answer

distance between 86Kr and 84Kr = 2*(R2 - R1)

= 2*(0.2646 - 0.2614)

= 0.0064 m or 6.4 mm <<<<<<<<---------Answer

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.