After 40 days have passed, how many grams of a 250-g sample of thorium-234 would remain?

78.78 g out of 250 g of Thorium-234 would remain after 40 days.

Explanation:

All radioactive samples are unstable in nature and so they will be decaying with time. So the equation of disintegration of the radioactive element is given as

So N is the mass of the radioactive element at time t and is the mass of the radioactive element at initial stage. Here k is the disintegration constant and t is the time.

We can determine the disintegration constant from the half life term of any element.

So,

Since, the half life time of thorium-234 is known to be 24 days. Then, the disintegration constant is

As the given questions have the initial mass as 250 g and t is given as 40 days, then the mass after 40 days will be

Thus, 78.78 g of thorium-234 would remain after 40 days.

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