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 Figure 27.24 in the textbook is 1.87×10^4 V/m and the magnetic field in both regions is 0.709 V.

If the source contains the three isotopes of krypton 82Kr, 84Kr and 86Kr 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 = 1 u = 1.66 * 10^-27 kg.)

Please don't just copy and paste the answer from the chapter because it's not correct.

Explanation / Answer

velocity   v   =   E / B   =   1.87 *10^4 V/m / 0.709 T v   =   2.64*10^4 m/s Under circular motion mv^2 / r     =   qvB radius of the circular orbit r   = mv / qB Here m = mass , v = vvelocity q = charge= 1.6*10^-19 C, B = magnetic field = 0.709 T diameter   of the circular orbit for 82 Kr D1   = 2r1   = m1 *v / qB diameter   of the circular orbit for 84 Kr D2 = 2r2   = m2 *v / qB diameter   of the circular orbit for 86 Kr D3 = 2r3   = m3 *v / qB distance between the 82 Kr and 84 Kr d =   m2 *v / qB   - m1 *v / qB    = v / qB   (m2 -m1)   .........(1) here m2 = 84*1.67*10^-27 kg , m1 =   82*1.67*10^-27 kg plug all values (1) we get d =  1.55 mm similarly distance between the 82 Kr and 84 Kr    d =   m3 *v / qB   - m2 *v / qB    = v / qB   (m3 -m2) here m3 =   86*1.67*10^-27 kg plug all values we get d = 1.55 mm diameter   of the circular orbit for 84 Kr D2 = 2r2   = m2 *v / qB diameter   of the circular orbit for 86 Kr D3 = 2r3   = m3 *v / qB diameter   of the circular orbit for 86 Kr D3 = 2r3   = m3 *v / qB distance between the 82 Kr and 84 Kr d =   m2 *v / qB   - m1 *v / qB    = v / qB   (m2 -m1)   .........(1) here m2 = 84*1.67*10^-27 kg , m1 =   82*1.67*10^-27 kg plug all values (1) we get d =  1.55 mm similarly distance between the 82 Kr and 84 Kr    d =   m3 *v / qB   - m2 *v / qB    = v / qB   (m3 -m2) here m3 =   86*1.67*10^-27 kg plug all values we get d = 1.55 mm

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