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

Question

asked Jul 3, 2019 150k views

1 Answer

James Mudd · Answer 1 · 2019-07-10T01:36:31+0000

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 = (60)/(30)

$\boxed{x = 2}$

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

m = (m_o)/(2^x)

m = (10)/(2^(2))

m = (10)/(4)

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

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