Question

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

Answer 1

Hint: Mass number is defined total number of protons and neutrons inside the nucleus. The mass of any element is due to the presence of protons and neutrons in the nucleus.
Protons are positively charged particles and neutrons have zero charge. Both particles are present in the nucleus.
Hence, Mass number = Number of protons + Number of neutrons

Complete step by step answer:
Let assume the number of protons to be hundred then according to the given percentage of neutrons 31.7 % more than protons the number of neutrons will be 131.7.
It mean if
P = 100 then N = 131.7……………..(i)
As atomic mass is given
A = 81 (A stands for atomic mass)
Then formula to calculate the atomic mass is,
A = P + N
P represents protons and N represents neutrons.
Putting the values in above equation,
$81 = P + N..........\left( ii \right)$
$N = 81 - P............\left( {iii} \right)$
Take the ratio of neutron and proton from eq (i),
$\dfrac{N}{P} = \dfrac{{131.7}}{{100}}...............\left( {iv} \right)$
Hence use equation $\left( {iii} \right)$ in equation $\left( {iv} \right)$ and divide the whole second equation by P,

$\dfrac{{131.7}}{{100}} = \dfrac{{81 - P}}{P}$

By cross multiplication
8100 - 100P = 131.7P
8100 = 100P + 131.7P
8100 = 231.7P

$P = \,\dfrac{{8100}}{{231.7}}$

$P = 34.5 \approx 35$
As we know
$Number\,\,of\,\,protons = Atomic\,\,number$
$_Z^AX = _{35}^{81}X = Br$

Note: The atomic number of bromine is 35 and mass number is 81.It belongs to a group of halogens and it exists in liquid state. As for the representation of any element we have to calculate its atomic number that is the number of protons. So the thing that we have to find always suppose it to be 100.