Correct Answer: Option A

Explanation

Fraction remaining of X   = (\(\frac{1}{2}\))\(^{\frac{t}{T_{\frac{1}{2}}}}\)

BUT \(\frac{t}{T_{\frac{1}{2}}}\) = \(\frac{200}{100}\) = 2

= (\(\frac{1}{2})^2\) = \(\frac{1}{4}\)

Fraction remaining of Y = (\(\frac{1}{2}\))\(^{\frac{t}{T_{\frac{1}{2}}}}\)

BUT \(\frac{t}{T_{\frac{1}{2}}}\) = \(\frac{200}{50}\) = 4

= (\(\frac{1}{2})^4\) = \(\frac{1}{16}\)

the ratio of the remaining atoms of  X to Y = \(\frac{X}{Y}\) = \(\frac{\frac{1}{4}}{\frac{1}{16}}\) =  \(\frac{1}{4}\) x  \(\frac{16}{1}\) = 4

Therefore, the ratio of the number of remaining atoms of  X to that of Y after 200 years is 4:1

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