Isotopes of Chlorine with mass number 35 and 37 exist in ratio?

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Solution

Isotope:
Isotopes are the atoms of the same element having different mass numbers and the same atomic number.
They have the same number of electrons and protons while the number of neutrons in each isotope is different.
Step 1: Considering the molecular weight of the isotopes:
The molecular weight of the isotope of Chlorine with an atomic mass of 35 can be taken as = $M_{1}$
The molecular weight of the isotope of Chlorine with atomic mass 37 can be taken as = $M_{2}$
Step 2: Considering the relative abundance of the isotopes:
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 = $100 - x$
Step 3:Formula for calculating the average molecular mass :
Now, Let's consider the average molecular weight to be $M$
Thus, average molecular mass can be calculated as;
$M = \frac{M_{1} \times x + M_{2} (100 - x)}{100}$
Step 4: Putting the values in the above formula to calculate the relative abundance of each isotope:
Now we will put the given values in the given formula and calculate the percentage existence of both the isotopes of Chlorine.
$\Rightarrow 35.5 = \frac{35 \times x + 37 (100 - x)}{100} \Rightarrow 3550 = 35 x + 37 (100 - x)$
On doing the simplification we have,
$\Rightarrow 3550 = 35 x + 3700 - 37 x \Rightarrow 37 x - 35 x = 3700 - 3500$
$\Rightarrow 2 x = 150 \Rightarrow x = 75$
Hence, we have got value for the relative abundance of the Chlorine of atomic mass 35 is $= 75$
We can calculate, the relative abundance of Chlorine with an atomic mass of 37 = $100 - x = 100 - 75 = 25$
Step 5: calculating the ratio of the relative abundance of two isotopes:
The ratio of Chlorine with atomic mass 35 to Chlorine 37 = $75 : 25$ = $3 : 1$

$∴$ Therefore the isotope of Chlorine with atomic mass 35 and 37 exists in the ratio of $3 : 1$

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Question 13

Chlorine exists in two isotopic forms. Cl - 37 and Cl - 35 but its atomic mass is 35.5. This indicates the ratio of Cl - 37 and Cl - 35 is approximately

(a) 1 : 2 (b) 1 : 1 (c) 1 : 3 (d) 3 : 1

Q. The isotopes of chlorine with mass numbers

35

and

37

whose average mass is 35.5 exist in the ratio of:

Q. 30 The isotopes of chlorine with mass number 35 and 37 exist in ratio if its average atomic mass is 35.5 of

_{17}^{35} C l

and

_{17}^{37} C l

are two isotopes of chlorine in mass ratio of

3 : x

, where

x

=

________.

Q. Chlorine exists in two isotopic forms,

C l - 37

and

C l - 35

but its atomic mass is

35.5

. This indicates the ratio of

C l - 37

and

C l - 35

is approximately:

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