It is found that 0.5 percent of radium dissappears in 12 years. What percentage will dissappears in 1000 years? What is the half life of radium?
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Let "x" be the quantity of radium at time "t".
Given, dtdx∝x
⇒dtdx=kx
xdx=kdt
Integrating on both sides, we get,
logx=kt+logc
logcx=kt
∴x=cekt
When t=0,x=A0
A0=cek×0
∴c=A0
When t=50,x=0.95A0
0.95A0=A0e50k
∴e50k=0.95
When t=100
x=A0e100k
=A0e50ke50k
=A0(0.95)(0.95)
=0.9025A
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