2 g of a radioactive sample having half-life of 15 days was synthesised on 1st Jan. 2009. What is the amount of the sample left behind on 1st March, 2009 (including both the days) in g?

Options

A. 0.125 g
B. 1 g
C. 0.5 g
D. 0g

Answer

A

Explanation

No. of days from `1^(st)` Jan 09 to `1^(st)` March '09 = 60
Given, `t_(1//2) = 15` days
Total time, `T = 60` days
`:.` No. of half-lives, n = ?
Also given, initial amount of sample, `N_(0) = 2g`
`:.` Sample present after 4 half lives, `N= ?`
`N = ((1)/(2))^(n) N_(0)`
`rArr N = ((1)/(2))^(4) xx 2 = (2)/(16) = 0.125g`