Question

The energy required to excite the hydrogen atom from its first excited state to second excited state is:

• A. 12.09 eV
• B. 1.89 eV
• C. 10.2 eV
• D. 3.40 eV
• E. 1.51 eV

Hint:

The energy required to excite a hydrogen atom between two levels is the difference between the energies of those levels.

Answer 1

The Correct Option is B

The energy required to excite a hydrogen atom between two energy levels is given by the difference in their energies. 
The energy of the nth orbit of a hydrogen atom is given by: \[ E_n = -\frac{13.6}{n^2} { eV} \] For the first excited state (\(n=2\)) and the second excited state (\(n=3\)): \[ E_2 = -\frac{13.6}{2^2} = -3.4 { eV} \] \[ E_3 = -\frac{13.6}{3^2} = -1.51 { eV} \] The energy required to excite the hydrogen atom from the first excited state to the second excited state is the difference: \[ \Delta E = E_3 - E_2 = (-1.51) - (-3.4) = 1.89 { eV} \] Thus, the energy required is 1.89 eV.