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?

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

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

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?

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

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

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?

$\frac{m}{q}=\frac{rB{B}_{selector}}{E_{selector}}$

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

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