Question

The minimum energy required to excite a hydrogen atom from its ground state is:
A. 3.4 eV
B. 13.6 eV
C. -13.6 eV
D. 10.2 eV

Answer 1

Hint: Hydrogen atoms have only one electron, then the energy required to excite a hydrogen atom will be equal to the energy required to excite one electron to the second level. We can then easily calculate the minimum energy required by substituting the value of n

Formula Used:
$E = - 13.6\dfrac{{{z^2}}}{{{n^2}}}$
where z is atomic number and n is energy state.

Complete answer:
Let’s start with defining the meaning of excited state and ground state. Ground state is the lowest energy level of the substance and it is the most stable state the substance is present in. Exiting state configuration is a higher energy configuration and is achieved when the energy is given to the substance at a ground state. We can also say that in the ground state the electrons of the atom are at lowest possible energy level and at the excited state the electrons of the atom are at an energy level higher than the lowest possible energy level.

Coming to the question we are given the hydrogen atom, since a hydrogen atom is having only one electron, then the energy required to excite a hydrogen atom will be equal to the energy required to excite one electron to the second level.
So, $E = - 13.6\dfrac{{{z^2}}}{{{n^2}}} = - 13.6 \times \dfrac{1}{{{n^2}}}$

Since we are using the energy level from 1 to 2, then
$E = - 13.6 \times (\dfrac{1}{{{2^2}}} - \dfrac{1}{{{1^2}}})$
Solving this we will get $E = 10.2eV$

Hence, the correct answer to this question is option D. 10.2 eV.

Note: The energy levels are studied just to get an idea regarding the stability of the molecule. The higher energy atoms and molecules are generally less stable and in case of molecules at higher energy levels the bonds between the two atoms get broken. So it is important to know the energy level of these molecules.