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

Answer:

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

Explanation:

Initial mass of the isotope = $N_o$

Time taken by the sample, t = $t_{\frac{1}{2}}$

Formula used :

$N=N_o\times e^{-\lambda t}\\\\\lambda =\frac{0.693}{t_{\frac{1}{2}}}$

where,

$N_o$ = initial mass of isotope

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

$t_{\frac{1}{2}}$ = half life of the isotope

$\lambda$ = rate constant

We have:

$t_{\frac{1}{2}}=28.8 years$

t = (2018 - 1945 )years = 73 years

So, on substituting the values:

$N=x\times e^{-(\frac{0.693}{28.8 years})\times 73 years}$

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

$N=N_o\times e^{-1.7566}$

$N=N_o\times 0.1726$

$\frac{N}{N_o}=0.1726$

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