Question

The ionization potential of a hydrogen is 13.6 eV. How much energy need to be supplied to ionize the hydrogen atom in the first excited state?

A.)13.6 eV
B.)27.2 eV
C.)3.4 eV
C.)6.8 eV

Answer 1

Hint:
There is a requirement of ionization energy for removal of each successive electron. We can find the energy in the $n^{th}$ shell of an atom by using the formula $\dfrac{1}{n^2}\times$(the ionization potential of that atom).

Complete step by step solution:
We have been given that the hydrogen atom is already in its first excited state and need to be ionized from there. So, we have to find the energy supplied or the energy supplied to ionize the hydrogen atom.

We can find the energy of the $n^{th}$ cell of a hydrogen atom by using the formula $\dfrac{1}{n^2}\times 13.6\; eV$.

So, its energy in the 1st excited state that is in n=2 will be $\dfrac{1}{2^2}\times 13.6\; eV=3.4\;eV$

So, in order to ionize the hydrogen atom from its first excited state, 3.4 eV of energy is needed to be supplied.

Hence option c is the correct answer.

Addition information:
Ionization potential or ionization energy is the amount of energy needed to be supplied to remove an electron from an atom or a molecule. Its magnitude is often dependent on the electric charge of the nucleus, its electronic configuration and size of the atom. The ionization potential keeps on increasing as we successively remove each electron. Ionization energy also determines the capability of an element to take part in a chemical reaction which requires ion formation or electron donation.

Note:
We should note that the amount of energy released or supplied for an electron to jump from one shell to another is different from the ionization energy of that electron. The electron jumps from one orbit to another is determined by the excitation energy and someone with an unclear concept may confuse it with the excitation energy.