Question

Sr-90 may be produced from an atomic bomb explosion. The half-life of Sr-90 is 28.8 years. What fraction of the Sr-90 originally produced by the first atomic bomb in July 1945 still remains as of July 2018?

Answer 1

The fraction of Sr-90 left after 73 years is 0.1726

Step-by-step explanation:

Initial mass of the isotope =
`N_o`

Time taken by the sample, t =
`t_{(1)/(2)}`

Formula used :

`N=N_o* e^(-\lambda t)\\\\\lambda =\frac{0.693}{t_{(1)/(2)}}`

where,

`N_o` = initial mass of isotope

N = mass of the parent isotope left after the time, (t)

`t_{(1)/(2)}` = half life of the isotope

`\lambda` = rate constant

We have:

`t_{(1)/(2)}=28.8 years`

t = (2018 - 1945 )years = 73 years

So, on substituting the values:

`N=x* e^{-((0.693)/(28.8 years))* 73 years}`

Now put all the given values in this formula, we get

`N=N_o* e^(-1.7566)`

`N=N_o* 0.1726`

`(N)/(N_o)=0.1726`

The fraction of Sr-90 left after 73 years = 0.1726