The wavelength of the first spectral line of an element is \( 5893\,\mathring{\mathrm{A}} \). The first excitation energy is :
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 2.1 eV
The first spectral line is emitted when the atom falls from the first excited level to the ground level. The photon energy equals the gap between these levels, which is the first excitation energy.
\( \displaystyle E = \frac{hc}{\lambda} \)
Using \( hc = 12400\,\mathrm{eV\,\mathring{A}} \) (that is, \( 1240\,\mathrm{eV\,nm} \)):
\( \displaystyle E = \frac{12400\,\mathrm{eV\,\mathring{A}}}{5893\,\mathring{\mathrm{A}}} = 2.10\,\mathrm{eV} \approx 2.1\,\mathrm{eV} \)