Question

The isotopes of chlorine with mass numbers 35 and 37 whose average mass is 35.5 exist in the ratio of:
A.$1:1$
B.$3:1$
C.$3:4$
D.$3:2$

Answer 1

Hint: Isotopes are the variants of a particular chemical element that differ in the neutron number and consequently in nucleon number. All isotopes of a given element have the same number of protons but a different number of neutrons in each atom. The term isotope is from the Greek roots isos which means equal and topos which means the same place. Thus, the meaning behind the name tells that isotopes of a single element occupy the same position in the periodic table.

Complete step by step answer:
Now we will calculate the ratio of chlorine.
Let us consider the percentage of the chlorine with atomic mass 35 be x and the percentage of the chlorine with atomic mass 37 be $100 - x$.
Now, Let the average molecular weight be M.
The molecular weight of the isotope of chlorine with atomic mass 35 be ${M_1}$
The molecular weight of the isotope of chlorine with atomic mass 37 be ${M_2}$
The relative abundance of the isotope of chlorine with atomic mass 35 be x
The relative abundance of the isotope of chlorine with atomic mass 37 is $100 - x$
 Now,
  $M = \dfrac{{{M_1} \times x + {M_2}\left( {100 - x} \right)}}{{100}}$
Now we will put the given values in the given formula and calculate the percentage existence of both the isotopes of chlorine.
 $ \Rightarrow 35.5 = \dfrac{{35 \times x + 37\left( {100 - x} \right)}}{{100}}
   \Rightarrow 3550 = 35x\, + 37\left( {100 - x} \right) $
And hence on doing the simplification we have,
  $ \Rightarrow 3550 = \,35x + 3700 - 37x
   \Rightarrow 37x - 35x = 3700 - 3500 $
(We have taken the x variable one at the other side to calculate the value of x)
 $ \Rightarrow 2x = 150
   \Rightarrow x = 75 $
After calculating we have got value for the percentage existence of the chlorine of atomic mass 35.
We know, the percentage existence of chlorine with atomic mass 37 is $100 - x = 100 - 75 = 25$
The ratio of chlorine with atomic mass 35 to chlorine 37 is $75:25$
It can be written as $3:1$
Therefore the isotope of chlorine with atomic mass 35 and 37 exists in the ratio of $3:1$
Hence, the correct option is (B).

Note:
Chlorine is an element of Group 17 from p-block elements. The Group 17 elements are – Fluorine, Chlorine, Bromine, Iodine, and Astatine. They are very reactive non-metals. They together form a family called the halogen family. They do not occur free in nature. All these elements have seven electrons in their valence shell (one electron less than that required for inert gas configuration).