A radioisotope has a half-life of 5 minutes. Initially, 10 g was present. What amount of the original atoms will be unchanged after 5 minutes?

Answer 1

Since the half life is given as 5 minutes, and the question ask how much is left after 5 minutes (1 half life), it would simply be 1/2 of the original amount.

1/2 of 10 g = 5 g will remain unchanged.

Mathematically, it would look like this:

fraction remaining = 0.5ⁿ where n = number of half lives that have elapsed.

fraction remaining = 0.5¹ = 0.5

0.5 x 10 g = 5 g

Answer 2

Hi Khadajah K.,

The half-life means the time it takes (1/2) of the atoms initially present to decay (by radioactive emission). Therefore, (1/2) of the initial amount will be left unchanged after 5 minutes.

That's a simple application of the concept; actually a radioactive material decays such that the remaining amount at time t, M(t), is related to the initial amount M(0) by: M(t) = M(0)*e^(-kt) . That is to say, the substance remaining follows an exponentially decreasing course towards zero.

By the way, that's a very "hot" isotope there; special techniques would be required to work with it. In my scientific career (analytical chemist), the shortest-half-life material I ever encountered had a 6-hr half-life (Tc99m). It is used for various organ blood-flow visualization -- it is imaged on its first pass through the organ, before it goes on to mix with all the rest of the blood in the body.

-- Cheers, -- Mr. d.