The average molar mass of chlorine is $$35.5\,\text{g mol}^{-1}$$. The ratio of $$^{35}\text{Cl}$$ to $$^{37}\text{Cl}$$ in naturally occurring chlorine is close to:

We know that naturally occurring chlorine is a mixture of two stable isotopes, $$^{35}\text{Cl}$$ and $$^{37}\text{Cl}$$. Their atomic (isotopic) masses are, to a very good approximation, $$35\,\text{u}$$ and $$37\,\text{u}$$ respectively.

The weighted (average) molar mass that appears on the periodic table is obtained by taking a mole-weighted mean of the individual isotopic masses. The general formula for the average molar mass $$\overline{M}$$ of a two-isotope mixture is

$$\overline{M}=\frac{n_{1}M_{1}+n_{2}M_{2}}{n_{1}+n_{2}},$$

where

$$n_{1},\,n_{2}\;=\;$$ number of moles (or any proportional measure) of the two isotopes $$,$$

$$M_{1},\,M_{2}\;=\;$$ their respective molar masses $$.$$

In our case

$$M_{1}=35\;\text{g mol}^{-1},$$ $$M_{2}=37\;\text{g mol}^{-1},$$ $$\overline{M}=35.5\;\text{g mol}^{-1}.$$

Let the amount of $$^{35}\text{Cl}$$ be $$n_{1}$$ and that of $$^{37}\text{Cl}$$ be $$n_{2}$$. Substituting the known values into the formula gives

$$35.5=\frac{35\,n_{1}+37\,n_{2}}{n_{1}+n_{2}}.$$

Because only the ratio is required, we may set $$n_{2}=1$$ (any convenient reference) and denote $$n_{1}=r$$, so that the sought ratio $$^{35}\text{Cl}:^{37}\text{Cl}=r:1$$. Rewriting the equation with these symbols, we have

$$35.5=\frac{35\,r+37\cdot1}{r+1}.$$

Now we clear the denominator by multiplying both sides by $$r+1$$:

$$35.5\,(r+1)=35\,r+37.$$

Expanding the left side,

$$35.5\,r+35.5=35\,r+37.$$

Next we collect like terms, bringing all expressions involving $$r$$ to the left and constants to the right:

$$35.5\,r-35\,r=37-35.5.$$

The left side simplifies to $$0.5\,r$$ and the right side to $$1.5$$, so

$$0.5\,r=1.5.$$

Dividing both sides by $$0.5$$ yields

$$r=\frac{1.5}{0.5}=3.$$

Therefore the ratio of $$^{35}\text{Cl}$$ to $$^{37}\text{Cl}$$ is

$$^{35}\text{Cl}:^{37}\text{Cl}=3:1.$$

Among the options provided, the ratio $$3:1$$ corresponds to Option B.

Hence, the correct answer is Option B.