Given an element with an average atomic mass of 35.5 and isotopes of mass numbers 35 and 37, calculate the relative abundance of the isotope with mass number 37.

The average atomic mass of an element is calculated by taking the weighted average of the masses of its isotopes.
Let $x$ be the relative abundance (in percent) of the isotope with mass number 35.
Then, the relative abundance of the isotope with mass number 37 will be $(100 - x)$ percent.
The formula for average atomic mass is:

$$\text{Average Atomic Mass} = \frac{(\text{Mass}_1 \times \text{Abundance}_1) + (\text{Mass}_2 \times \text{Abundance}_2)}{100}$$

Given:

• Average atomic mass = 35.5
• Mass of isotope 1 = 35
• Mass of isotope 2 = 37

Substitute these values into the formula:

$$35.5 = \frac{(35 \times x) + (37 \times (100 - x))}{100}$$

Multiply both sides by 100:

$$35.5 \times 100 = 35x + 37(100 - x)$$ $$3550 = 35x + 3700 - 37x$$

Combine the $x$ terms:

$$3550 = (35x - 37x) + 3700$$ $$3550 = -2x + 3700$$

Subtract 3700 from both sides:

$$3550 - 3700 = -2x$$ $$-150 = -2x$$

Divide by -2:

$$x = \frac{-150}{-2}$$ $$x = 75$$

So, the relative abundance of the isotope with mass number 35 is $75\%$.

The relative abundance of the isotope with mass number 37 is $(100 - x)\%$.

$$\text{Abundance of isotope 37} = 100\% - 75\%$$ $$\text{Abundance of isotope 37} = 25\%$$

The relative abundance of the isotope of mass number 37 is $25\%$.

The final answer is $\text{D}$.