A modern version of Bertozzi's experiment is set up to measure the relativistic properties of high-speed electrons. A pulsed beam of electrons is accelerated from rest through a potential difference (pd) of 1.50 MV1.50 \text{ MV}1.50 MV and directed towards a copper block detector.
Show that each electron gains approximately 2.4×10−13 J2.4 \times 10^{-13} \text{ J}2.4×10−13 J of kinetic energy.
The pulse of electrons causes the temperature of a 2.00 kg2.00 \text{ kg}2.00 kg copper block to increase by 171 K171 \text{ K}171 K. The total number of electrons in the pulse is 5.50×10175.50 \times 10^{17}5.50×1017.
Deduce whether this observed temperature increase is consistent with an accelerating pd of 1.50 MV1.50 \text{ MV}1.50 MV.
The speed of the electrons between the accelerator's final exit stage and the detector block is measured to be 2.90×108 m s−12.90 \times 10^8 \text{ m s}^{-1}2.90×108 m s−1.
Evaluate both suggestions using calculations of the kinetic energy of an electron at this speed.
A laboratory timer records the time taken for the electron pulse to travel from the exit detector to the copper block as 35.0 ns35.0 \text{ ns}35.0 ns.
What is the proper time interval for an electron travelling this distance?
The electrons were accelerated from rest in 151515 stages, each using a pd of 100 kV100 \text{ kV}100 kV.
Compare, for an electron:
Justify your answer. No further calculations are required.
