Question

Name: Christina Gonzalez PARTI - Hydrogen, energy levels, and atomic line spectra Lab Worksheet - Atomic Theory 1.a) Electrons in an atom are more stable than free electrons. This is why the energy levels of electrons in atoms are negative (free electrons are defined as having an energy of zero). Calculate the energy of a hydrogen electron in the 4th shell, in J. b) Calculate this energy in kJ/mole.

Answer 1

(a) Energy of an electron in n^th shell of the hydrogen atom can be calculated by the following formula:

E_n = -R_H (1/n²)

where, R_H is a constant value of 2.179 x 10^-18 Joules and n represents the shell or level whose energy is being calculated.

So for n= 4 : E_n = -2.179 x 10^-18 Joules X (1/16) = 1.36 x 10^-19 Joules

(b) The above value in J can be converted to kJ/mol.

1.36 x 10^-19 Joules is the energy of a single electron in the 4th shell. To find the energy of 1 mole of electrons we need to multiply our answer with Avogadro's number

(6.022 X 10²³ electrons / 1 mole electrons)  X (1.36 x 10^-19 J / 1 electron) X (1 kJ/ 10³ J)

= 81.9 kJ/mol

Similarly, the energy of electron in other shells can also be calculated by changing the value of n.

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