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The total number of electrons in 4.2 g of ${N^{3 - }}$ ion is : (${N_A}$ is the Avogadro’s number )
a.) 2.1${N_A}$
b.) 4.2${N_A}$
c.) 3${N_A}$
d.) 3.2${N_A}$


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Last updated date: 13th Jun 2024
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Answer
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Hint: We can calculate the number of moles of nitrogen.
Number of moles = $\dfrac{{Given{\text{ mass}}}}{{Molar{\text{ mass}}}}$
Further, we know that a neutral nitrogen atom has 7 electrons. But in this, the nitrogen has a negative charge of 3. So, the total number of electrons in nitrogen is 10.
1 mole of an element = Number of electrons in element $ \times {N_A}$
Thus, we can calculate the number of electrons.

Complete step by step answer :
The number of electrons in an atom can be determined from the atomic number of an atom. A neutral atom of an element has the number of electrons equal to the atomic number of the element.
Here, the element is Nitrogen. The nitrogen has atomic number 7. Thus, a neutral nitrogen atom has 7 electrons. But in this, the nitrogen has a negative charge of 3. So, the negative charge corresponds to the gain of electrons. This means three extra electrons are there in the nitrogen atom.
So, the total number of electrons in the nitrogen atom is 10.
We are given with mass of nitrogen = 4.2 g
From this, we can calculate the number of moles of nitrogen.
Number of moles = $\dfrac{{Given{\text{ mass}}}}{{Molar{\text{ mass}}}}$
Number of moles = $\dfrac{{4.2g}}{{14g}}$
Number of moles = 0.3 moles
1 mole of ${N^{3 - }}$ = 10 $ \times {N_A}$
0.3 moles = 0.3 $ \times 10 \times {N_A}$
0.3 moles = $3 \times {N_A}$

Thus, the correct answer is the option c.).

Note: It must be noted that the negative charge on an atom means that the number of electrons have been gained by the atom and needed to be added and by positive charge means that number of electrons have been donated by the atom which is to be subtracted from the atom.