Question

There are three stable isotopes of magnesium. Their masses are 23.9850, 24.9858, and 25.9826 u. If the average atomic mass of magnesium is 24.3050 u and the natural abundance of the lightest isotope is 78.99%, what are the natural abundances of the other two isotopes?

Answer 1

Answer:

²⁵ Mg = 10.00%

²⁶ Mg = 11.0%

Explanation:

Given that:

Magnesium ²⁴Mg has an abundance of 78.99%

Hence, (100 - 78.99)% = 21.01%

21.01% is the abundance of ²⁵ Mg and ²⁶ Mg

Suppose,

²⁵ Mg = x

²⁶ Mg = (21.01 - x)%

Then;

avg. atomic mass = $\dfrac{78.99}{100 }(23.9850)+\dfrac{x}{100}(24.9858) +\dfrac{21.01-x}{100}(25.9826)$

where the avg. atomic mass = 24.3050

∴

$24.3050 \times 100 = {78.99}(23.9850)+\dfrac{x}{100}(24.9858) +\dfrac{21.01-x}{100}(25.9826)$

2430.5 = 2440.46915 -0.9968 x

0.9968x = 2440.46915 - 2430.5

0.9968x = 9.96915

x  =  9.96915/0.9968

x  =  10.00%

∴ Recall that:

²⁵ Mg = x

²⁶ Mg = (21.01 - x)%

²⁵ Mg = 10.00%

²⁶ Mg = (21.01 - 10.00)%

²⁶ Mg = 11.0%