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Exercises · 2.42

Q.An element with mass number 81 contains 31.7% more neutrons as compared to protons. Assign the atomic symbol.

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Solving n=1.317 pn = 1.317\,p together with p+n=81p + n = 81 gives p=35p = 35, so the element is bromine. The symbol is 3581Br^{81}_{35}\text{Br}.

Let pp = number of protons and nn = number of neutrons.

Neutron–proton relation ("31.7% more neutrons than protons"):

n=p+0.317 p=1.317 pn = p + 0.317\,p = 1.317\,p

Mass-number constraint:

p+n=81p + n = 81

Substitute and solve:

p+1.317 p=81⇒2.317 p=81⇒p=812.317≈35p + 1.317\,p = 81 \quad\Rightarrow\quad 2.317\,p = 81 \quad\Rightarrow\quad p = \frac{81}{2.317} \approx 35 …

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