Question

A sample of ore containing radioactive strontium 38Sr90 has an activity of 8.2 × 105 Bq. The atomic mass of strontium is 89.908 u, and its half-life is 28.8 yr (1 yr = 3.156 × 107 s). How many grams of strontium are in the sample?

Answer 1

From the activity values and the decay constant, the mass of of Strontium in the sample is:

$1.62 × 10^{-7}g$

What is the decay constant of an element?

The decay constant of an element is the probability of decay of a nucleus per unit time.

{λ = ln 2 / t1/2 

where;

t1/2 is the half-life of the isotope.

The half-life is converted to seconds since the decay constant is asked in per seconds.

$28.8 years = 28.8 × 3.156 × 10^{7} = 908928000 s$

Hence;

$λ = \frac{ln2}{90892800s} = 7.626 s^{-1}$

                                       

The activity of the element, A, the decay constant, λ and the number of nuclei, N are related as follows:

• A = (–) λN

$N = \frac{8.25 ×10^{5}}{7.626×10^{-10}} = 1.082 × 10^{15}$              

Molar mass of Strontium-90 is 90 g.

1 mole of Strontium-90 contains 6.02×10^23 nuclei.

The mass, m of Strontium in the sample is calculated:

$m = 1.082 × 10^{15} × \frac{90 g}{6.02 × 10^{23}} = 1.62 × 10^{-7}g$

Therefore, the mass of of Strontium in the sample is:

$1.62 × 10^{-7} \: g$

Learn more about decay constant at: brainly.com/question/17159453