Question

The energy required for the ionisation of $0.02$ gram atom of magnesium is $x\;KJ$. The amount of energy required to ionise 1 atom of magnesium is:
a.) $x\;KJ$
b.) $\dfrac{{x}}{{0.02{N_A}}}J$
c.) $\dfrac{{x \times {{10}^3}}}{{0.02{N_A}}}J$
d.) $x{N_A}KJ$

Answer 1

o solve the above problem, firstly we will calculate the number of the moles of the magnesium with the help of the given mass and the molecular mass of the magnesium. Then we will get the total number of the atoms of the magnesium after that we will calculate the energy required to ionise one atom.
Molecular mass of the magnesium, ${m_{Mg}} = 24$

Complete step by step answer:
Now we will calculate the number of the moles of the magnesium and we all know that the number of the moles can be calculated by dividing the given mass by the molecular mass of the element.
Hence the number of the moles of the magnesium= $\dfrac{{Given{\text{ }}mass}}{{Molecular{\text{ }}mass}}$=$\dfrac{{0.02}}{{24 \times 100}} = \dfrac{1}{{1200}}$
Now we multiply the number of the moles with the Avogadro’s number $({N_A})$ then we will get the number of the atoms.

We know that the Avogadro’s number is denoted by ${N_A}$.
So, the number of the atoms of the magnesium= $\dfrac{{{N_A}}}{{1200}}$
Now it is given in the question that,
$\dfrac{{{N_A}}}{{1200}}$ atoms require energy of $x\;KJ$ to get ionised.
Hence the energy required by the one atom to get ionise = $\dfrac{{x\;}}{{\left( {\dfrac{{{N_A}}}{{1200}}} \right)}}KJ$
$= \dfrac{{x \times {{10}^3}\;}}{{\left( {\dfrac{{{N_A}}}{{1200}}} \right)}}J$
$= \dfrac{{x \times {{10}^3}\;}}{{{N_A} \times \left( {\dfrac{1}{{1200}}} \right)}}J$
$= \dfrac{{x \times {{10}^3}\;}}{{0.02{N_A}}}J$
Hence, the amount of energy required to ionise 1 atom of magnesium is $\dfrac{{x \times {{10}^3}\;}}{{0.02{N_A}}}J$.
So, the correct answer is “Option A”.

Note: Ionisation is the process by which an atom or a molecule acquires a negative or positive charge by gaining or losing electrons, often in conjunction with other chemical changes while the Ionization energy is the quantity of energy that an isolated, gaseous atom in the ground electronic state must absorb to discharge an electron, resulting in a cation. This energy is usually expressed in kJ/mol, or the amount of energy it takes for all the atoms in a mole to lose one electron each.