Question

The ionization energy of hydrogen is 13.6eV. The energy of the photons released when an electron jumps from the first excited state (n = 2) to the ground state of a hydrogen atom is
A. 3.4eV
B. 4.56eV
C. 10.2eV
D. 13.6eV

Answer 1

Hint: The energy required to remove the most loosely bound electron, the valence electron, of an isolated neutral gaseous atom or molecule. We have given the energy ${E_1}$ of hydrogen. We can find the energy when an electron jumps from first excited state to the ground state by ${E_2} = \dfrac{{ - 13.6}}{{{n^2}}}$, where n = 2.

Complete answer:
Now, from the question
We have given, ${E_1}$ = -13.6eV
Now energy of first excited state (n = 2) is

${E_2} = \dfrac{{ - 13.6}}{{{n^2}}}$
${E_2} = \dfrac{{ - 13.6}}{{{2^2}}} = \dfrac{{ - 13.6}}{4} = - 3.4eV$

Now, the energy of photons released when an electron jumps from the first excited state to the ground state is ${E_2} - {E_1} = - 3.4 - ( - 13.6) = - 3.4 + 13.6 = 10.2eV$

So, the correct answer is “Option C”.

Additional Information:
Factors Governing Ionization Energy =
Normally, when the ionization energy is high it'll be harder to get rid of an electron. There also are several factors that govern the attraction forces.

1. If the nucleus is charged then the electrons are strongly interested in it.
2. If an electron lies near or on the brink of the nucleus then the attractions are going to be greater than the one when the electron is further away.
3. If there are more electrons between the outer level and therefore the nucleus the attraction forces are less.
4. When there are two electrons within the same orbital they experience some sort of repulsion. Now, this creates disturbances within the attraction of the nucleus. In essence, ionization energy are going to be less in paired electrons as they will be removed easily.

Note:
In more technical terms we will describe ionization energy the minimum energy that an electron during a gaseous atom or ion needs to absorb to return out of the influence of the nucleus. It's also sometimes mentioned as ionization potential and is typically an endothermic process.

What we will deduce further is that ionization energy gives us a thought of the reactivity of chemical compounds. It also can be wont to determine the strength of chemical bonds. It's measured either in units of electron volts or$\dfrac{{kJ}}{{mol}}$. Depending on the ionization of molecules which frequently results in changes in molecular geometry, ionization energy is often either adiabatic ionization energy or vertical ionization energy.