# Question b342a

Jun 13, 2015

$\Delta E = \text{+1260. kJ/mol}$

#### Explanation:

The energy of the ${n}^{t h}$ Bohr orbit for a hydrogen atom, which has $Z = 1$, is given by the equation

${E}_{n} = {E}_{1} / {n}^{2}$, where

${E}_{1}$ - the energy of the ${1}^{s t}$ Bohr orbit, equal to $\text{-1312 kJ/mol}$;
$n$ - the energy level;

In your case, the energy of the fifth energy level will be

${E}_{5} = {E}_{1} / {5}^{2} = {E}_{1} / 25$

E_5 = ("-1312 kJ/mol")/25 = "-52.48 kJ/mol"#

Therefore, the difference between ${E}_{5}$ and ${E}_{1}$ will be

$\Delta E = {E}_{5} - {E}_{1}$

$\Delta E = - \text{52.48 kJ/mol" -(-"1312 kJ/mol") = "+1259.5 kJ/mol}$

Rounded to four sig figs, the answer will be

$\Delta E = \textcolor{g r e e n}{\text{+1260. kJ/mol}}$

This tells you that, in order to get 1 mole of electrons from the first energy level to the fifth energy level in a hydrogen atom, you need to provide 1260. kJ.