In the ground state of the Hydrogen atom the energy of the electron is E 0 = -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 = 43 from the periodic table. Ionize it 42 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 = 20 principal state in the ion above?

Explanation / Answer

Eo = -13,61 eV

E = Eo*Z^2/n^2

for He Z =2

for ground state n =1

E = -13.61*4/1 = -54.44 eV

for Li , Z =3

for ground state n =1

E =-13.61*9/1 = -122.49 eV

for n =2, He

E = -13.61*4/4 = -13.61 eV

for Li , Z =3

for n =2

E = -13.61*3^2/2^2 = -30.62 eV

for n= 3

E = -13.61*9/9 = -13.61 eV

Z = 43

E = -13.61*43^2/1 = -25164.89 eV

for n = 20

E = -13.61*43^2/20^2 = -62.9 eV

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