2. As calculated in the Bohr model, the speed of the electron in the ground state of
a hydrogen-like atom or ion of atomic number Z, v(Z), is given by the equation
υ(Ζ) = e^2Z/(4πε₀ħ) = Zac where a = e^2/(4πε₀ħc) ≈ 1/137. We denote the
corresponding non-relativistic kinetic energy by Knrel (Z) and the corresponding
relativistic kinetic energy by Krel(Z).
(a) Sketch a graph of log10[Knrel(Z)/(13.6 eV)] vs. log10(Z) for Z varying from
1 to 100. Briefly explain why the difference between the mass of the
electron and the reduced mass of the atom or ion is negligible for this
graph. [6 marks]
(b) The figure below is meant to show how the ratio Krel(Z)/Knrel(Z) varies
with Z over a certain range of values of Z. Discuss whether this graph is
accurate. [4 marks]
1.6
A
Krel/Knrel
1.4
1.2
1.0
65
Z
82