Question

Substance $X$ has three common isotopes: $X-48,X-49$ and $X-51$. If the relative abundances of these three isotopes are $42$%, $38$% and $20$% respectively, what is the atomic mass of substance $X$?

• A. $49.33$ amu
• B. $48.62$ amu
  
• C. $50.67$ amu
  
• D. $48.98$ amu
  
• E. $49.67$ amu
  

Answer 1

The correct option is D $48.98$ amu

$X$ has three isotopes $X-48$, $X-49$ and $X-51$. The relative abundances of the three isotopes are $42$%, $38$% and $20$%.

$X-48$ represents that the weight of the isotope is let's say $48amu$.

Thus $42$% of $X-48$ will weigh $\frac{42}{100}$$\times$$48$, that is $20.16amu$

$X-49$ represents that the weight of the isotope is let's say $49amu$.

Thus, $38$% of $X-49$ will weigh $\frac{38}{100}$$\times$$49$, that is $18.62amu$.

$X-51$ represents that the weight of the isotope is let's say $51amu$.

Thus, $20$% of it will weigh $\frac{20}{100}\times 51$, that is $10.2amu$.

Thus, the total weight of the substance is $(20.16+18.62+10.2)$, that is $48.98amu$

Option D is the correct answer.