Correct Answer: Option C

Explanation

Initial Mass: 512 g, Mass Decayed: \(\frac{7}{8}\) of 512 = 448g, Remaining mass = 512 - 448 = 64g

Using, N(t) = No(\(\frac{1}{2}\))\(^{\frac{T}{T1/2}}\)

\(\frac{N(t)}{No}\) = (\(\frac{1}{2}\))\(^{\frac{T}{T1/2}}\)

\(\frac{64}{512}\) = \(\frac{1}{8}\) =  (\(\frac{1}{2}\))\(^{\frac{T}{15}}\)

\(\frac{1}{8}\) = (\(\frac{1}{2}\))\(^3\) =  (\(\frac{1}{2}\))\(^{\frac{T}{15}}\)

equating coefficient

3 = \(\frac{T}{15}\)

T = 3 x 15 = 45hours.

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