Question

You have 480 grams of a radioactive kind of samarium. If its half-life is 90 years,

Answer 1

Answer:

120 grams will be left after 180 years.

Step-by-step explanation:

A radioactive half-life refers to the amount of time it takes for half of the original isotope to decay and its given by

                                             $N(t)=N_0(\frac{1}{2})^\frac{t}{t_{1/2}}$

where,

$N(t)$ = quantity of the substance remaining

$N_0$ = initial quantity of the substance

$t$ = time elapsed

$t_{1/2}$ = half life of the substance

From the information given we know that:

• The initial quantity is 480 g,
• The half-life is 90 years,
• 180 years is the time elapsed.

And we want to find how much will be left. For this we use the above formula.

$N(t)=480\left(\frac{1}{2}\right)^{\frac{180}{90}}\\\\N(t)=480\left(\frac{1}{2}\right)^2\\\\N(t)=480\cdot \frac{1}{2^2}=120$

120 grams will be left after 180 years.