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 = 47 from the periodic table. Ionize it 46 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 = 8 principal state in the ion above?

Explanation / Answer

(a) The energy of the electron in the ground state of the He+ ion is given as ::

E = - (13.61 eV) Z2 / n2                                                                                   { eq.1 }

where, Z = atomic number of helium = 2

n = principal state = 1

inserting these values in above eq.

E = - (13.61 eV) (2)2 / (1)2

E = - 54.44 eV

(b) The energy of the electron in the ground state of the Li++ ion is given as ::

E = - (13.61 eV) Z2 / n2         

where, Z = atomic number of lithium = 3

n = principal state = 1

E = - (13.61 eV) (3)2 / (1)2

E = - 122.49 eV

(c) The energy of the electron now which is given as ::

For He+ ion, n = principal state = 2 , Z = atomis number = 2

then, E = - (13.61 eV) (2)2 / (2)2

E = - 13.61 eV

(d) The energy of the electron in the Li++ ion in the n = 2 principal state which is given as ::

E = - (13.61 eV) (3)2 / (2)2

E = - 30.62 eV

(e) The energy of the electron in the Li++ ion in the n = 3 principal state which is given as ::

E = - (13.61 eV) (3)2 / (3)2

E = - 13.61 eV

(f) The ground state energy of the electron will be given as ::

For Z = 47 from the periodic table.

n = 1   (principle state)

E = - (13.61 eV) (47)2 / (1)2

E = - 30064.4 eV

(g) The energy of the electron, when it is in the n = 8 principal state in the ion above which given as ::

E = - (13.61 eV) (47)2 / (8)2

E = - (30064.4 / 64) eV

E = - 469.7 eV

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