Question

Calculate % abundance of Ag109 if it is known that silver exist
in only two isotopes
Ag 107& Ag109 having average atomic weight = 108.5​

Answer 1

$\red{\bigstar}\underline{\underline{\textsf{\textbf{ Given :- }}}}$

• Silver exists in two isotopic form , Ag 109 and Ag 107.
• It has a average Atomic mass of 108.5.

$\red{\bigstar}\underline{\underline{\textsf{\textbf{ To Find :- }}}}$

• The percentage of each isotope .

$\red{\bigstar}\underline{\underline{\textsf{\textbf{ Solution :- }}}}$

We need to find out the percentage abundance of each isotopes. For that let us assume that the percentage of first isotope is x % and that of second is (100 - x)% .

$\sf\longrightarrow \% of \ Ag \ 109 \ = \ x \\\\\sf\longrightarrow \% of \ Ag \ 107 \ = \ (100 - x )$

We know that , we can calculte the average Atomic mass by.

$\sf\longrightarrow Avg. \ Atomic\ Mass \ = \dfrac{ (\% \ of \ 1st \ isotope )(Atomic\ Mass ) + (\% \ of \ 2nd \ isotope )(Atomic\ Mass ) }{100} \\\\\\\sf\longrightarrow 108.5 = \dfrac{ x*109 + 107*(100-x)}{100} \\\\\\\sf\longrightarrow 109x + 10700 - 107x = 108.5 * 100 \\\\\\\sf\longrightarrow 2x = 10850 - 10700 \\\\\\\sf\longrightarrow 2x = 150 \\\\\\\sf\longrightarrow x = 150\div 2 \\\\\\\sf\longrightarrow \boxed{\pink{\frak{\quad x \quad = \quad 75\% }}}\quad \star$

Therefore ,

$\sf\longrightarrow \% \ of \ Ag \ 109 \ = \ x =\red{75\%} \\\\\sf\longrightarrow \% \ of \ Ag \ 107 \ = \ (100 - x )= \red{25\%}$

Answer 2

Explanation:

this is the explaination of the answer