A dimensionless number that often appears in atomic physics is the fine$-$structure constant

$,$ given by$,$

$=\text{'}$

$4-$

a$)(3$ pts$)$ Obtain a numerical value for $1/.$

b$)(3$ pts$)$ In scattering experiments, the $$size$$ of the electron is the classical electron

radius,

$-=1$

$4-$

$\text{'}$

$1\text{'}$

In terms of $,$ what is the ratio of the Compton wavelength, $=/1,$ to the

classical electron radius?

c$)(3$ pts$)$ In terms of $,$ what is the ratio of the Bohr radius, $-,$ to the Compton

wavelength?

d$)(3$ pts$)$ In terms of $,$ what is the ratio of the Rydberg wavelength, $1/,$ to the Bohr

radius?