(a) What is the ionization energy of a hydrogen atom that is in the n = 6 excited state? (b) For a hydrogen atom, determine the ratio of the ionization energy for the n = 6 excited state to the ionization energy for the ground state.

Answer :

Answer:

(a) 0.3778 eV

(b) Ratio = 0.0278

Explanation:

The Bohr's formula for the calculation of the energy of the electron in nth orbit is:

[tex]E=\frac {-13.6}{n^2}\ eV[/tex]

(a) The energy of the electron in n= 6 excited state is:

[tex]E=\frac {-13.6}{6^2}\ eV[/tex]

[tex]E=-0.3778\ eV[/tex]

Ionisation energy is the amount of this energy required to remove the electron. Thus, |E| = 0.3778 eV

(b) For first orbit energy is:

[tex]E=\frac {-13.6}{1^2}\ eV[/tex]

[tex]E=-13.6\ eV[/tex]

[tex]Ratio=\frac {E_6}{E_1}[/tex]

[tex]Ratio=\frac {-0.3778}{-13.6}[/tex]

Ratio = 0.0278