Question

Calculate number of neutrons present in \[12 \times {10^{25}}\] atoms of oxygen\[\left( {_8{O^{17}}} \right)\]: Given \[\left[ {{N_A} = 6 \times {{10}^{23}}} \right]\]
A. \[1800\]
B. \[1600\]
C. \[1800\;{N_A}\]
D. \[3200\;{N_A}\]

Answer 1

Hint:
We know that the fundamental unit of matter is an atom; it is composed of three particles, protons, neutrons and electrons. There are heavier protons and neutrons than electrons, and they are present in the core of the atom, called the nucleus. The number of atoms can be determined by using two quantities one of them is Avogadro’s number and the other one is the respective molar mass of all the species.

Complete step by step solution
We know that atomic number is equal to the number of protons hence,
\[
{\rm{Atomic}}\;{\rm{number}} = {\rm{number}}\;{\rm{of}}\;{\rm{protons}}\\
{\rm{Atomic}}\;{\rm{number}} = 8
\]
And we know that mass number is the addition of the number of protons and number of neutrons.
\[{\rm{Mass}}\;{\rm{number}} = {\rm{Number}}\;{\rm{of}}\;{\rm{proton}}\; + {\rm{number}}\;{\rm{of}}\;{\rm{neutron}}\]
According to the question , we know that mass number is \[17\], hence substituting we get.
\[
{\rm{Mass}}\;{\rm{number}} = {\rm{Number}}\;{\rm{of}}\;{\rm{proton}}\; + {\rm{number}}\;{\rm{of}}\;{\rm{neutron}}\\
17 = 8 + {\rm{number}}\;{\rm{of}}\;{\rm{neutron}}\\
{\rm{Number}}\;{\rm{of}}\;{\rm{neutron}} = 17 - 8\\
 = 9
\]
Here we find the number of neutrons; we have to calculate the number of neutrons present in \[12 \times {10^{25}}\] of oxygen.
To calculate the total number of neutrons in \[12 \times {10^{25}}\] atoms of oxygen.
\[
{\rm{Therefore,}}\;{\rm{total}}\;{\rm{number}}\;{\rm{of}}\;{\rm{neutrons}} = 9 \times 12 \times {10^{25}}\\
 = 108\; \times {10^{25}}\;{\rm{neutrons}}
\]
We know that \[{N_{\rm{A}}} = 6 \times {10^{23}}\;{\rm{atoms}}\]
\[
{\rm{In}}\;{\rm{term}}\;{\rm{of}}\;{N_{\rm{A}}}\;{\rm{we}}\;{\rm{can}}\;{\rm{write}}\;{\rm{it}}\;{\rm{as}} = \frac{{108 \times {{10}^{25}}}}{{6 \times {{10}^{23}}}}\\
 = 18 \times {10^2}\\
 = 1800\;{N_{\rm{A}}}
\]

Therefore, the correct answer is C.

Note:
Electrons have negative charge, protons have positive charge and neutrons have no any charge. The discovery of the electron was done by J J Thomson, the proton is discovered by Rutherford and neutron by Chadwick. Proton and neutron is present in the nucleus, due to the charge of proton the nucleus also overall positive charge. Electrons are surrounding the nucleus. We can say that an atom is neutral because the atom number of proton and the number of electrons are equal so they cancel each other, hence, the atom is neutral.