Question

Zirconium has an atomic number of $40$. How many neutrons are there in an isotope of zirconium-$92$ ?

Answer 1

Hint: In order to solve this equation we first need to know, the relationship between protons, electrons and neutrons of an element. The number of protons is equal to the atomic number. Isotopes of any given element contain the same number of protons, therefore they have the same atomic number but contain different numbers of neutrons, hence, different isotopes have different mass numbers.

Complete step-by-step answer:
From the question it is understood that the atomic number is $40$ which is denoted as ‘Z’ and atomic mass is $92$ which is denoted as ‘M’ of zirconium. The approximation of mass can be used to calculate how many neutrons an element has, which is done by subtracting the number of protons which is the same as the atomic number from the mass number. Protons and neutrons both weigh one atomic mass unit or amu. Isotopes of the same element will have the same atomic number but can have different mass numbers.
The equation to find the number of neutrons is given by,
$$\begin{gathered} M-Z=N \\ 92-40=52 \end{gathered}$$
Hence, we can conclude that there are $52$ neutrons in an isotope of zirconium-$92$

Additional information:
Isotopes can be defined as the variants of chemical elements that have the same number of protons and electrons, but different numbers of neutrons. Or in other words we can say isotopes are variants of elements that differ in their nucleon numbers because of a difference in the total number of neutrons in their respective nuclei.

Note: Isotopes are atoms of the same element that have different neutron number but has the same number of protons and electrons. The difference in the number of neutrons between the various isotopes of an element shows us that the various isotopes can have different masses. The superscript number to the left of the element abbreviation indicates the number of protons plus neutrons in the isotope. The mass number of an atom is equal to the sum of the number of protons and the neutrons contained in its nucleus.