A-level Physics (Advancing Physics)/Cloud Chambers and Mass Spectrometers/Worked Solutions

Charge of electron = -1.6 x 10-19C

Mass of electron = 9.11 x 10-31kg

u = 1.66 x 10-27kg

1. An electron enters a cloud chamber, passing into a 0.1T magnetic field. The initial curvature (the reciprocal of its radius) of its path is 100m-1. At what speed was it moving when it entered the magnetic field?

$r = \frac{mv}{qB}$

$v = \frac{qBr}{m} = \frac{1.6 \times 10^{-19} \times 0.1 \times 0.01}{9.11 \times 10^{-31}} = 1.76 \times 10^8\mbox{ ms}^{-1} = 0.585c$

This is too close to the speed of light to ignore special relativity, however we just did.

2. The electron spirals inwards in a clockwise direction, as show in the diagram on the right. What would the path of a positron, moving with an identical speed, look like?

3. Using a 2T magnetic field, what electric field strength must be used to get a velocity selector to select only particles which are moving at 100ms-1?

$v = \frac{E}{B}$

$E = Bv = 2 \times 100 = 200\mbox{ Vm}^{-1}$

4. Some uranium (atomic number 92) ions (charge +3e) of various isotopes are put through the velocity selector described in question 3. They then enter an 0.00002T uniform magnetic field. What radius of circular motion would uranium-235 have?

$\frac{m}{q} = \frac{rBB_{selector}}{E_{selector}}$

$\frac{235 \times 1.66 \times 10^{-27}}{3 \times 1.6 \times 10^{-19}} = r \times \frac{2 \times 0.00002}{200} = 0.0000002r$

$r = \frac{235 \times 1.66 \times 10^{-27}}{0.0000002 \times 3 \times 1.6 \times 10^{-19}} = 4.06\mbox{ m}$