BITSAT 2015 Paper

Let the initial mass of uranium be M0 Final mass of uranium after time t,
M =

3

4

M0
According to the law of radioactive disintegration

M

M0

= (

1

2

)t∕T ⇒

M0

M

= (2)t∕T
∴ log10(

M0

M

) =

t

T

log10 (2)
t = T

log10( M0 M )

log10(2)

=

Tlog10( 4 3 )

log10(2)

=

Tlog10(1.333)

log10(2)

= 4.5 × 109(

0.1249

0.3010

)
⇒ t = 1.867 × 109 yr.