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The half-life of radium is 16000 yr, aft...

The half-life of radium is 16000 yr, after how much time will 1 g radium be reduced to 125 mg?

A

800 yr

B

1600 yr

C

3200 yr

D

4800 yr

Text Solution

Verified by Experts

The correct Answer is:
d
Given, `t_(1//2) = 1600 yr, N_(0) = 1 g, N = 125 mg = (125)/(1000)g`
We know that, `N = N_(0)((1)/(2))^((t)/(t_(1//2)))`
`(125)/(1000) = ((1)/(2))^(t//1600), (1)/(8) or ((1)/(2))^(3) = ((1)/(2))^(t//1600)`
Hence, `(t)/(1600) = 3 or t = 3xx1600 = 4800 yr`
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