Question

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

Answer 1

Hint:As we have already learnt that number of electrons in an atom is equal to the number of protons. And the number of protons along with the number of neutrons is equal to the mass number of an atom.

Complete answer:
The basic thing that we know is the number of electrons in an atom is equal to the number of protons. And the number of protons along with the number of neutrons is equal to the mass number of an atom or we can say that the number of neutrons in an atom can be calculated by subtracting the proton number from its atomic mass.
To calculate the number of neutrons, we can subtract the mass number of the atom from the atomic number of that atom. We also know that atomic number is represented as Z and atomic mass as A, neutrons are represented as N and protons are represented as P. Oxygen possesses atomic number 8, mass number or atomic mass 17. So, using the formula to calculate the number of neutrons in one atom of oxygen:
$
  N = A - Z \\
\Rightarrow N = 17 - 8 \\
\Rightarrow N = 9
 $
Now, to calculate the total number of neutrons in $12 \times {10^{25}}$atoms of oxygen, we can simply multiply the number of neutrons In one atom with this, doing the same we get:
Total number of neutrons:
$
\Rightarrow n = 9 \times 12 \times {10^{25}} \\
\Rightarrow n = 108 \times {10^{25}}
 $
We are also given with Avogadro’s number in the question, so in terms of Avogadro’s number:
$
\Rightarrow n = \dfrac{{108 \times {{10}^{25}}}}{{6 \times {{10}^{23}}}} \\
\Rightarrow n = 1800{N_A}
 $

Therefore from the above solution we can say that the correct answer is option (C).

Note:
Neutrons are tiny particles found within the nucleus in all atoms except hydrogen. There are Neutrons stars present that are the result of a massive collapsed star. They are the smallest and dense stellar objects known. The first neutron star that was discovered with planets is the PSR B1257+12 which is a millisecond pulsar.