**A sample of tritium is decayed to 89.3% of its original amount after 2 years. What is the half life? How long would it take the sample to decay to 20% of the original amount?**

**Answer:**

t1/2 = t * ln(2)/ln(N0/Nt)

where,

t1/2 = half time

t=time gone by = 2 years

N0= initial count = 100

Nt = final count = 89.3

ln is natural log (base e)

putting the values we get…

t1/2 = 2 x ln(2)/ ln(100/89.3)

=2 x 0.693 / 0.113

=12.26 years (Half life)

now to calculate t20 or the time taken to decay to 20% of original

t20= 2 x ln(100/20) / ln (100/89.3)

= 2 x 1.609/0.113

=28.47 years