Question

An element X occurs in nature in three isotopic forms with masses 30u, 32u and 33 u in the ratio 3:3:4. What is the average mass of element X?

• A. 31.80
• B. 32.10
• C. 33.20
• D. 30.10

Answer 1

The correct option is A

31.80

The isotopes with masses 30u, 32u and 33u in the ratio 3:3:4.

The average mass can be calculated in following manner,

Consider the ratio 3:3:4,

The contribution of isotope having mass 30u, 32u and 33 u to average atomic mass will respectively be in the ratio 3/10, 3/10, 4/10 respectively.

i.e. contribution of isotope of mass 30 u will be $30\times$ $\frac{3}{10}$

similarly, contribution of isotope of mass 32 u will be $32\times$$\frac{3}{10}$

contribution of isotope of mass 30 u will be $33\times$$\frac{4}{10}$

Therefore average atomic mass will be :

Z= $30\times$ $\frac{3}{10}$+$32\times$$\frac{3}{10}$+$33\times$$\frac{4}{10}$

$\Rightarrow$ Z= $\frac{90}{10}$+$\frac{96}{10}$+$\frac{132}{10}$

$\Rightarrow$ Z= $\frac{318}{10}$

$\Rightarrow$ Z= 31.80