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:

$T = x*P$

$80 = x*20$

$80 = 20\:x$

$20\:x = 80$

$x = \dfrac{80}{20}$

$\boxed{x = 4}$

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

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

$m = \dfrac{43}{2^{4}}$

$m = \dfrac{43}{16}$

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

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