Q. how to calculate number of neutrons

Step 1. Know the basic formula. The number of neutrons in a nucleus, denoted \(N\), is the mass number minus the atomic number. In LaTeX form, this is

\[
N = A – Z
\]

Explain the symbols. \(A\) is the mass number, which equals the total number of nucleons, that is, protons plus neutrons. \(Z\) is the atomic number, which equals the number of protons. For any isotope, the relation \(A = Z + N\) holds, so solving for \(N\) gives the formula above.

Step 2. Identify \(A\) and \(Z\) from the information given. Common ways these are provided:

– Nuclear notation: \(^{A}_{Z}\mathrm{X}\). The top number \(A\) is the mass number. The bottom number \(Z\) is the atomic number.

– Isotope name: \(\mathrm{Element}\text{-}A\), for example Carbon-14 means \(A=14\). The atomic number \(Z\) is the element’s proton count, found on the periodic table.

Step 3. Compute \(N\) using the formula. Subtract the atomic number from the mass number and report the result as an integer number of neutrons.

Worked example 1. Carbon-14. Carbon has atomic number \(Z=6\). The isotope Carbon-14 has mass number \(A=14\). Compute

\[
N = 14 – 6 = 8
\]

So Carbon-14 has 8 neutrons.

Worked example 2. Chlorine-37. Chlorine has atomic number \(Z=17\). For the isotope with \(A=37\),

\[
N = 37 – 17 = 20
\]

So Chlorine-37 has 20 neutrons.

Important note about atomic masses. The value listed as “atomic mass” on the periodic table is a weighted average of isotopic masses and is not generally an integer. You cannot use that average directly in \(N = A – Z\). To find neutrons you must use the mass number \(A\) of a specific isotope. If only an average atomic mass is given and no isotope is specified, you need additional information or must be told which isotope to use.

Summary procedure you can follow every time:

1. Determine the mass number \(A\) (from isotope notation or name). 2. Determine the atomic number \(Z\) (from the periodic table or given). 3. Calculate \(N = A – Z\).