Question

The ionization enthalpy of a hydrogen atom is $1.312 \times {10^6}J/mol$. The energy required to excited electron in an atom from $n = 1$ to $n = 2$is:
A.$7.56 \times {10^5}J/Mmol$
B.$9.84 \times {10^5}J/Mmol$
C.$8.51 \times {10^5}J/Mmol$
D.$6.56 \times {10^5}J/Mmol$

Answer 1

Hint:This question gives the knowledge about ionization enthalpy. The ionization enthalpy is defined as the minimum amount of energy required to remove the electron from the isolated gaseous atom in its ground state.
Formula used:
The formula used to determine the energy of an electron in a particular orbit is as follows:
${E_n} = \dfrac{{ - 1312}}{{{n^2}}}$
Where ${E_n}$ is the energy at the \[{n^{th}}\] level and $n$ is the orbit.

Complete step by step answer:
The ionization enthalpy is defined as the minimum amount of energy required to remove the electron from the isolated gaseous atom in its ground state.
Now we will determine the energy of an electron in the first orbit as follows:
$ \Rightarrow {E_n} = \dfrac{{ - 1312}}{{{n^2}}}$
Substitute $n$ as $1$ in the above formula.
$ \Rightarrow {E_1} = \dfrac{{ - 1312}}{{{1^2}}}$
On simplifying the above equation we get,
$ \Rightarrow {E_1} = - 1312$
The energy of the first orbit is $ - 1312kJ/mol$.
Now we will determine the energy of an electron in the second orbit as follows:
$ \Rightarrow {E_n} = \dfrac{{ - 1312}}{{{n^2}}}$
Substitute $n$ as $2$ in the above formula.
$ \Rightarrow {E_2} = \dfrac{{ - 1312}}{{{2^2}}}$
On simplifying the above equation we get,
$ \Rightarrow {E_2} = - 328$
The energy of the first orbit is $ - 328kJ/mol$.
So, the energy required by the excited electron is the difference between these two orbits.
Therefore, the energy required by the excited electron is $ - 984kJ/mol$. And in terms of joules the energy required is $9.84 \times {10^5}J/Mmol$.

Hence, option $B$ is the correct option.

Note:
The ionization enthalpy is defined as the minimum amount of energy required to remove the electron from the isolated gaseous atom in its ground state. Periodic table is basically the tabular representation of elements, which are organized by electronic configuration, atomic number and repeated chemical properties. Periodic table consists of seven rows and eighteen groups. In rows, the elements are organized from left to right and in groups, elements are organized from top to bottom. In total there are $118$ elements present in the periodic table. . In the periodic table, ionization energy decreases the group.