Question

The half-life of radium is 1590 year. If 10 grams is present now, how much will be present in 50 years?

Answer 1

`20(1/2)^(1640/1590)=9.78439` gm, nearly.7.13 gm, nearly

Explanation:

The decay equation is

`m = m_0e^(-kt)`,

where `m_0` is mass at t = 0.

Given #m_0/2=10 ahen t = 1590,

m_0=20 and

`10=20 (e^-k)^1590`, giving `e^(-k)=(1/2)^(1/1590)`

At t = 1590+50=1640,

`m=20(e^-k)^1640=20(1/2)^(1640/1590)=9.78439` gm, nearly.