Exercises for Chapter 12 281(12.5) Production of highly-charged ions in an EBIT
(a) Estimate the accelerating voltage required for
an electron beam voltage that produces hy-
drogenic silicon Si13+in an EBIT.
(b) Calculate the radius of the first Bohr orbit
(n= 1) in hydrogenic uranium, U+91.
(c) Calculate the binding energy of the electron in
U+91and express it as a fraction of the atom’s
rest mass energyMc^2.
(d) QED effects contribute 3× 10 −^5 eV to thebinding energy of the 1s ground configuration
of atomic hydrogen. Express this as a frac-
tion of the hydrogen atom’s rest mass. Esti-
mate the magnitude of the QED contribution
in the ground state of hydrogen-like uranium
U+91as a fraction of the rest mass. This frac-
tion gives the precision ∆M/Mwith which
the ion’s mass must be determined in order to
measure QED effects. Discuss the feasibility
of doing this in an ion trap.Web site:
http://www.physics.ox.ac.uk/users/foot
This site has answers to some of the exercises, corrections and other supplementary information.