Question

half life of 90sr is t/2 28.8 years.how long it will take to decay all but 0.01% of a sample of a 90sr​

Answer 1

19 years that is after calculating only the given circumstances

Answer 2

Given info : half life of a sample of Sr is 28.8 years.

To find : the time at which it will decay all but 0.01% of the sample.

solution : given, half life = 28.8 years

we know, radioactive decay is first order reaction.

so, half life is given by, T½ = ln2/k

where K is radioactive decay constant.

now 28.8 years = ln2/k

⇒k = ln2/28.8 year¯¹ ....(1)

now using formula,

t = 1/k ln[a]₀/[a]t

here [a]t = 0.01 % of [a]₀ = 10¯⁴[a]₀

from equations (1),

so, t = 1/(ln2/28.8) ln(10⁴)

= 28.8/ln2 × 4 × ln(10)

= 28.8 × 4 × 2.30258/0.6931

= 382.71 years

Therefore time will be taken is 382.71 years.