Question

The minimum excitation energy of an electron revolving in the first orbit of hydrogen is:

• A. 3.4 eV
• B. 8.5 eV
• C. 10.2 eV
• D. 13.6 eV

Hint:

Excitation energy is the energy required to move an electron from a lower to a higher energy level.

Answer 1

The Correct Option is C

Step 1: {Energy Levels in the Hydrogen Atom}
The energy of an electron in the \( n^{th} \) orbit is: \[ E_n = \frac{-13.6}{n^2} { eV} \] For \( n = 1 \): \[ E_1 = -13.6 { eV} \] For \( n = 2 \): \[ E_2 = \frac{-13.6}{4} = -3.4 { eV} \] Step 2: {Calculating Excitation Energy}
\[ E_{{excitation}} = E_2 - E_1 \] \[ = (-3.4) - (-13.6) \] \[ = 10.2 { eV} \] Thus, the correct answer is \( 10.2 \) eV.

Answer 2

Step 1: Understanding Excitation Energy
The excitation energy of an electron is the energy required to raise it from a lower energy level to a higher one in an atom.

Step 2: Energy Levels in Hydrogen Atom
The energy of the electron in the \( n^\text{th} \) orbit of hydrogen is given by: \[ E_n = -\frac{13.6}{n^2} \, \text{eV} \]

For the first orbit (\( n = 1 \)): \[ E_1 = -13.6 \, \text{eV} \]

For the second orbit (\( n = 2 \)): \[ E_2 = -\frac{13.6}{2^2} = -3.4 \, \text{eV} \]

Step 3: Minimum Excitation Energy
The minimum excitation energy is the energy required to excite the electron from the first orbit to the second orbit: \[ \Delta E = E_2 - E_1 = (-3.4) - (-13.6) = 10.2 \, \text{eV} \]

Final Answer:
\[ \boxed{10.2 \, \text{eV}} \] Hence, the correct option is:

Option 3: 10.2 eV