The energy required (in eV) to excite an electron of H-atom from the ground state to the third state is
Show Hint
For hydrogen atom,
\[
E_n=\frac{-13.6}{n^2}\,\text{eV}
\]
Excitation energy is always calculated using
\[
\Delta E=E_f-E_i
\]
where \(E_f\) is the final energy level and \(E_i\) is the initial energy level.
Step 1: Write the energy formula for hydrogen atom. The energy of an electron in the nth orbit is: \[ E_n = \frac{-13.6}{n^2} \text{ eV} \] Lower orbits have more negative energy. Step 2: Find the energy in the ground state (n = 1). \[ E_1 = \frac{-13.6}{1^2} = -13.6 \text{ eV} \] Step 3: Find the energy in the third state (n = 3). \[ E_3 = \frac{-13.6}{9} = -1.51 \text{ eV} \] Step 4: Calculate the energy required for excitation. \[ \Delta E = E_3 - E_1 = -1.51 - (-13.6) = 12.09 \text{ eV} \] Step 5: Round to significant figures. \[ \Delta E \approx 12.1 \text{ eV} \] A positive value means energy must be absorbed to excite the electron upward. Step 6: State the final answer. The energy required to excite from n=1 to n=3 is +12.1 eV. \[ \boxed{12.1 \text{ eV}} \]