Question

Strontium 90 is a radioactive material that decays according to the function Upper A (t )equals Upper A 0 e Superscript negative 0.0244 t Baseline comma where Upper A 0 is the initial amount present and A is the amount present at time t​ (in years). Assume that a scientist has a sample of 800 grams of strontium 90. ​(a) What is the decay rate of strontium​ 90? ​(b) How much strontium 90 is left after 10 ​years? ​(c) When will only 600 grams of strontium 90 be​ left? ​(d) What is the​ half-life of strontium​ 90?

Answer 1

Answer:

a) λ = 0.0244 y⁻¹

b) 627 g

c) 11.8 years

d) 28.4 years

Explanation:

Strontium 90 is a radioactive material that decays according to the function

$A(t)=A_{0}.e^{-0.0244t}$

where,

A(t) is the amount present at time t​ (in years)

A₀ is the initial amount present

0.0244 is the decay rate λ

Assume that a scientist has a sample of 800 grams of strontium 90. ​(a) What is the decay rate of strontium​ 90?

​(a) What is the decay rate of strontium​ 90?

According to the exponential decay function, the decay rate is λ = 0.0244 years⁻¹

​(b) How much strontium 90 is left after 10 ​years?

If A₀ is 800 g and t is 10 years, A(t) is:

$A(t)=800g.e^{-0.0244\times 10}=627g$

​(c) When will only 600 grams of strontium 90 be​ left?

If A₀ is 800 g and A(t) is 600 g, t is:

$600g=800g.e^{-0.0244t}\\t=11.8y$

(d) What is the​ half-life of strontium​ 90?

We can calculate half-life using the following expression.

$t_{1/2}=\frac{ln2}{\lambda } =\frac{ln2}{0.0244y^{-1} } =28.4y$