The electron’s path while in the region of magnetic field is a quarter circle. Show that the

(i) speed of the electron after acceleration is 9.4×10⁶ms⁻¹.

(ii) radius of the path is 4.5×10⁻⁴m.

The diagram below shows the momentum of the electron as it enters and leaves the region of magnetic field. The magnitude of the initial momentum and of the final momentum is 8.6×10⁻²⁴Ns.

(i) On the diagram above, draw an arrow to indicate the vector representing the change in the momentum of the electron.

(ii) Show that the magnitude of the change in the momentum of the electron is 1.2×10⁻²³Ns.

(iii) The time the electron spends in the region of magnetic field is 7.5 ×10⁻¹¹s. Estimate the magnitude of the average force on the electron.

(i) \(v = \sqrt {\frac{{2eV}}{m}} \);
\(v = \sqrt {\frac{{2 \times 1.6 \times {{10}^{ - 19}} \times 250}}{{9.1 \times {{10}^{ - 31}}}}} \);
=9.4×10⁶ms⁻¹

(ii) evB=m\(\frac{{{v^2}}}{r}\);
\(r = \frac{{9.1 \times {{10}^{ - 31}} \times 9.4 \times {{10}^6}}}{{1.6 \times {{10}^{ - 19}} \times 0.12}}\);
=4.5×10⁻⁴m

(i) vector as shown;

(ii) \(\Delta p = \sqrt {{{\left[ {8.6 \times {{10}^{ - 24}}} \right]}^2} + {{\left[ {8.6 \times {{10}^{ - 24}}} \right]}^2}} \);
=1.2×10⁻²³Ns

(iii) \(F\left( { = \frac{{\Delta p}}{{\Delta t}} = \frac{{1.2 \times {{10}^{ - 23}}}}{{7.5 \times {{10}^{ - 11}}}}} \right) = 1.6 \times {10^{ - 13}}{\rm{N}}\);