Question $8$: boltzmann$\_$v$1$

An electron is trapped using lasers $($you don't need to know details about this!$).$ All you need to know is that the electron has $3$ states, with energies as follows:

State $1$: $6\mathrm{.}1$ eV

State $2$: $6\mathrm{.}2$ eV

State $3$: $6\mathrm{.}4$ eV

It is in equilibrium with a reservoir at temperature $1106$ K$.$

What is the probability that the electron is in state $1?$

$($a$)$

$1\mathrm{.}63$e$-28$

$($b$)$

$7\mathrm{.}18$e$-01$

$($c$)$

$1\mathrm{.}56$e$-02$

$($d$)$

$3\mathrm{.}33$e$-01$

$($e$)$

$2\mathrm{.}27$e$-28$

What is the entropy of the electron as the temperature T$$ $?$

$($a$)$

$9\mathrm{.}47$e$-05$ eV$/$K

$($b$)$

$1\mathrm{.}10$e$+00$ eV$/$K

$($c$)$

$1\mathrm{.}00$e$+00$ eV$/$K

$($d$)$

$5\mathrm{.}97$e$-05$ eV$/$K

$($e$)$

$0\mathrm{.}00$e$+00$ eV$/$K