Question

The half-life of radium is 1690 years. If 50 grams are present now, how much will be present in 800 years?

Answer 1

In order to determine the amount of radium after 800 years, use the following formula:

$N=N_oe^{-\lambda t}$

where,

N: amount of radium after t years = ?

No: initial amount of radium = 50g

λ: decay constant

t = 800

The decay constant is calculated by using the following expression:

$\lambda=\frac{ln2}{t\frac{_1}{2}}=\frac{ln2}{1960}\approx3.5*10^{-4}$

where t1/2 = 1960 is the half-life.

Now, by replacing λ, No and t = 800 you obtain:

$N=50e^{-(3.5*10-4)(800)}\approx37.68g$

Hence, after 800 years there are approximately 37.68g of uranium