Question

The half-life of radium-226 is 1590 years. if a sample contains 100 mg, how many mg will remain after 3000 years?

Answer 1

Hello!

The half-life is the time of half-disintegration, it is the time in which half of the atoms of an isotope disintegrate.

We have the following data:

mo (initial mass) = 100 mg

m (final mass after time T) = ? (in mg)

x (number of periods elapsed) = ?

P (Half-life) = 1590 years

T (Elapsed time for sample reduction) = 3000 years

Let's find the number of periods elapsed (x), let us see:

$T = x*P$

$3000 = x*1590$

$3000 = 1590\:x$

$1590\:x = 3000$

$x = \dfrac{3000}{1590}$

$\boxed{x \approx 1.8868}$

Now, let's find the final mass (m) of this isotope after the elapsed time, let's see:

$m = \dfrac{m_o}{2^x}$

$m = \dfrac{100}{2^{1.8868}}$

$m \approx \dfrac{100}{3.698}$

$\boxed{\boxed{m \approx 27.041\:mg}}\end{array}}\qquad\checkmark$

I Hope this helps, greetings ... DexteR! =)