Question

If there are 180 grams of radioactive material with a half-life (decrease by half or 50%) of 1 hour, how much of the radioactive material will be left after 3 hours?

Answer 1

Answer:

After 3 hours there is left 22.5 grams of radioactive material.

Step-by-step explanation:

We can calculate the mass of radioactive material remaining after 3 hours, by using the decay equation:           

$N_{t} = N_{0}*e^{-\lambda t}$     (1)

Where:

$N_{0}$: is the initial mass = 180 g

$N_{t}$: is the remaining mass after time t

λ: is the decay constant

The decay constant is given by:

$\lambda = \frac{ln(2)}{t_{1/2}}$

Where $t_{1/2}$ = 1 h.

By entering λ into equation (1) we hve:

$N_{t} = N_{0}*e^{-\frac{ln(2)}{t_{1/2}} t}$

$N_{t} = 180 g*e^{-\frac{ln(2)}{1 h} 3 h} = 22.5 g$

Therefore, after 3 hours there is left 22.5 grams of radioactive material.

I hope it helps you!