solve 24 plzz

24. The half-life of a radioactive isotope is three hours. If the initial mass of the isotope was 300 gm, the mass which remained undecayed in 18 hours would be
(a) 2.34 gm
(b) 1.17 gm
(c) 9.36 gm
(d) 4.68 gm

Dear student,

Since the initial concentration is given to be 300 gm and half life is 3 hours. It means that every 3 hours, the concentration becomes half of the initial amount.

Hence for total time of 18 hours, the reaction proceeds as:

300 g $\stackrel{3 hours}{\to }$    150 g $\stackrel{6 hours}{\to }$     75 g $\stackrel{9 hours}{\to }$    37.5 g $\stackrel{12 hours}{\to }$    18.75 g $\stackrel{15 hours}{\to }$    9.375 g $\stackrel{18 hours}{\to }$     4.6875 g 

Hence at the end of 18 hours, there will be 4.68 g of element left undecayed.

The correct answer is option (d).

Regards!