Question #b342a

1 Answer
Stefan V.
Jun 13, 2015

#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.

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