Question

Suppose the half life of an isotope is 30 seconds and you have 10 grams to start with how much will you have after one minute

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) = 10 g

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

x (number of periods elapsed) = ?

P (Half-life) = 30 seconds

T (Elapsed time for sample reduction) = 1 minute → 60 seconds

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

$T = x*P$

$60 = x*30$

$60 = 30\:x$

$30\:x = 60$

$x = \dfrac{60}{30}$

$\boxed{x = 2}$

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

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

$m = \dfrac{10}{2^{2}}$

$m = \dfrac{10}{4}$

$\boxed{\boxed{m = 2.5\:g}}\end{array}}\qquad\checkmark$

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