Question

It is found that 0.5 percent of radium disappears in 12 years. What percentage will disappear in 1000 years? what is the half life of Radium?​

Answer 1

Answer:

Answer

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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