A mass spectrometer is used to compare a neutral atom of calcium-40 with the doubly…
PHYSICS · Multi-part · A Level · Physics · Particles and radiation · Particles and radiation
Problem
A mass spectrometer is used to compare a neutral atom of calcium-40 with the doubly ionized ion Ca2+ of the same isotope. Both particles move at the same speed before entering a uniform magnetic field that bends their trajectories into semicircular paths of equal radius.
Relevant physical constants:
• Elementary charge e=1.60×10−19C
• Electron mass =9.11×10−31kg
• 1 u =1.66×10−27kg
(1) Determine the approximate mass, in kilograms, of a neutral calcium-40 atom using the integer-mass approximation.
(2) Using the constants above, calculate the approximate mass, in kilograms, of a Ca2+ ion of the same isotope.
(3) Express the mass difference between the neutral atom and the ion as a percentage of the neutral atomic mass. Comment on why the spectrometer can treat the two masses as essentially identical for trajectory comparison at the stated precision of one part in 104. (No numerical work is required beyond the percentage you calculate.)