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 1.85*10^4V/m and the magnetic field in both regions is 0.665T .(Figure 1)

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 = 1.6610^?27 kg.)

Express your answer using two significant figures.

d=?m

Suppose the electric field between the plates P and P' in the mass spectrometer in following figure is 1.85*10^4V/m and the magnetic field in both regions is 0.665T .(Figure 1) f 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 = 1.66½10^?27 kg.) Express your answer using two significant figures. d=?m Velocity selector selects particles with speed v. Magnetic field separates particles by mass; the greater a particle?s mass, the larger is the radius of its path.

Explanation / Answer

first to find the velocity

qvB=qE

==> v= E/B= 1.85E4/0.665=2.782 E4 m/s

now the radius of the path

R=mv/qB

==> distance between two adjecent line = 2*(R2-R1)= 2*(m2-m1)*v/qB = 2*(84-82)*1.67E-27*2.782E4/(1.6E-19*0.665)

==> d =0.00174 m = 1.74 mm

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