Question

Question #b342a

Answer 1

`DeltaE = "+1260. kJ/mol"`

Explanation:

The energy of the `n^(th)` 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^(st)` Bohr orbit, equal to `"-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

`DeltaE = E_5 - E_1`

`DeltaE = -"52.48 kJ/mol" -(-"1312 kJ/mol") = "+1259.5 kJ/mol"`

Rounded to four sig figs, the answer will be

`DeltaE = color(green)("+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.