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

Last updated date: 10th Aug 2024
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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.

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.
$\ M - Z = N \\ 92 - 40 = 52 \\ \\ \$
Hence, we can conclude that there are $52$ neutrons in an isotope of zirconium-$92$