The binding energy of a hydrogen atom is inversely proportional to the square of the principal quantum number n.The binding energy of the ground level of atomic hydrogen is 13.6 eV.The binding energy of the second (n = 2)level of the hydrogen atom is
A)+13.6 eV
B)-13.6 eV
C)-3.4 eV
D)-54.8 eV
E)+3.4 eV

Question

Quizplus · Accepted Answer

According to the given information, binding energy is inversely proportional to the square of the principal quantum number n. 
So, we can write: 
Binding Energy ∝ 1/n² 
Using this, we can find the binding energy of the second level of hydrogen atom: 
13.6 eV ∝ 1/1² 
Binding energy of the second level ∝ 1/2² = 1/4 
So, Binding energy of the second level = 13.6 eV x 1/4 = 3.4 eV 
Therefore, the correct choice is C, which is -3.4 eV in the negative direction.

The Binding Energy of a Hydrogen Atom Is Inversely Proportional