Question

If the ionisation energy for the hydrogen atom is \(13.6\) eV, then the energy required to excite it from the ground state to the next higher state is nearly

• A. \(-10.2\,eV\)
• B. \(-3.4\,eV\)
• C. \(10.2\,eV\)
• D. \(13.6\,eV\)

Hint:

Energy levels are -13.6/n^2 eV, so the first excitation goes from n = 1 to n = 2.

Answer 1

The Correct Option is C

Step 1: Difference formula
$\Delta E = 13.6\left(\dfrac{1}{1^2} - \dfrac{1}{2^2}\right)$ eV.

Step 2: Evaluate
$13.6\times\dfrac{3}{4} = 10.2$ eV.

Step 3: Sign
Energy is absorbed in going up, so it is positive.

Step 4: Answer
Option (C).

Step 5: Why the sign and size matter
The hydrogen atom must absorb energy to move up a level, so the energy supplied is positive. The first excited state has $n = 2$, which is the next higher level above $n = 1$. The value 13.6 eV would ionise the atom completely rather than excite it to the next level, and the negative values are level energies, not energies to be supplied.

Final Answer:
The required energy is 10.2 eV. This is option (C). \[ \boxed{\text{(C) }10.2\ \text{eV}} \]