In the ground state of the Hydrogen atom the energy of the electron is E0 = -13.

Question

In the ground state of the Hydrogen atom the energy of the electron is E0 = -13.61 eV. What is the energy of the electron in the ground state of the He+ ion?

What is the energy of the electron in the ground state of the Li++ ion?

The electron in the He+ ion is excited to the n = 2 principal state. What is the energy of the electron now?

What is the energy of the electron in the Li++ ion in the n = 2 principal state?

What is the energy of the electron in the Li++ ion in the n = 3 principal state?

Take element Z = 12 from the periodic table. Ionize it 11 times so that there is only one electron left orbiting around the nucleus. What is the ground state energy of the electron?

What is the energy of the electron when it is in the n = 19 principal state in the ion above?

Explanation / Answer

energy of electron in n principal state in hydrogen like atom = -13.6*(Z/n)^2 eV

hence

1) energy of  electron in ground state in He+ = -13.6*(2/1)^2 eV = -54.4 eV

2) energy of  electron in ground state in Li++ = -13.6*(3/1) eV = -122.4 eV

3) energy of  electron in n=2 state in He+ =   -13.6*(2/2)^2 eV = -13.6 eV

4)  energy of  electron in n=2 state in Li++ =   -13.6*(3/2)^2 eV = -30.6 eV

5)  energy of  electron in n=3 state in Li++ =   -13.6*(3/3)^2 eV = -13.6 eV

6)  energy of  electron in ground state in z=12 hydrogen like ion =   -13.6*(12/1)^2 eV = -1958.4 eV

7)  energy of  electron in n=19 state in z=12 hydrogen like ion =   -13.6*(12/19)^2 eV = -5.42 eV

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