Element Q has two isotopes. The first isotope has a mass number of 14 and an abundance of 99.63%. If the relative atomic mass of Q is 14.0037, what is the mass number of the second isotope?

The relative atomic mass of an element with multiple isotopes is calculated using the formula:

$$\text{Relative Atomic Mass} = \sum (\text{mass of isotope} \times \text{fractional abundance of isotope})$$

For two isotopes, this becomes:

$$\text{Relative Atomic Mass} = (A_1 \times P_1) + (A_2 \times P_2)$$

where $A_1$ and $A_2$ are the mass numbers of the isotopes, and $P_1$ and $P_2$ are their respective fractional abundances.

Given that element $Q$ has two isotopes and the abundance of the first isotope ($P_1$) is $99.63\%$.
The sum of the abundances of all isotopes must be $100\%$.

$$P_1 + P_2 = 100\%$$ $$99.63\% + P_2 = 100\%$$ $$P_2 = 100\% - 99.63\% = 0.37\%$$

Convert percentages to fractional abundances:

$$P_1 = \frac{99.63}{100} = 0.9963$$ $$P_2 = \frac{0.37}{100} = 0.0037$$

Given:
Relative Atomic Mass of $Q = 14.0037$
Mass number of the first isotope ($A_1$) = 14
Abundance of the first isotope ($P_1$) = 0.9963
Abundance of the second isotope ($P_2$) = 0.0037
Let the mass number of the second isotope be $A_2$.

$$14.0037 = (14 \times 0.9963) + (A_2 \times 0.0037)$$

$$14.0037 = 13.9482 + (A_2 \times 0.0037)$$

Subtract 13.9482 from both sides:

$$14.0037 - 13.9482 = A_2 \times 0.0037$$ $$0.0555 = A_2 \times 0.0037$$

Divide by 0.0037:

$$A_2 = \frac{0.0555}{0.0037}$$ $$A_2 = 15$$

The mass number of an isotope must be a whole number.

The mass number of the second isotope is $\text{15}$.