Question

A radioactive isotope of potassium (k) has a half-life of 20 minutes. if a 43 gram sample of this isotope is allowed to decay for 80 minutes, how many grams of the radioactive isotope will remain?

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) = 43 g

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

x (number of periods elapsed) = ?

P (Half-life) = 20 minutes

T (Elapsed time for sample reduction) = 80 minutes

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

`T = x*P`

`80 = x*20`

`80 = 20\:x`

`20\:x = 80`

`x = (80)/(20)`

`\boxed{x = 4}`

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

`m = (m_o)/(2^x)`

`m = (43)/(2^(4))`

`m = (43)/(16)`

`\boxed{\boxed{m = 2.6875\:g}}\end{array}}\qquad\checkmark`

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