A hydrogen atom is in its fourth excited state $($n $=5).$ Using the Bohr theory of the atom, calculate the following.

$($a$)$ the radius of the orbit

$($b$)$ the linear momentum of the electron

$($c$)$ the angular momentum of the electron

$($d$)$ the kinetic energy

$($e$)$ the potential energy

$($f$)$ the total energy

Step $1$

$($a$)$ According to the Bohr theory, the allowed orbits are determined by the integer n$.$ The radii of the allowed orbits are

rn $=$ n$2$a$0,$

where the Bohr radius a$0=0\mathrm{.}0529$ nm corresponds to the radius at n $=1.$ Thus, in the n $=5$ state, the radius of the orbit is

r$5=$

$2$

$0\mathrm{.}0529$ nm

$=$ nm$.$