Question about Radioactive Decay Rate

[Perkins]

.I was doing a radioactive decay problem and the solutions said that...

The radioactive decay per unit mass of an object is smaller when the age of the object is greater. The younger the object is, the faster the rate of radioactive decay.

Why is this statement true? I thought the rate of radioactive decay would be constant for an object?

Thanks!
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[ilovemcat]

.I was doing a radioactive decay problem and the solutions said that...

The radioactive decay per unit mass of an object is smaller when the age of the object is greater. The younger the object is, the faster the rate of radioactive decay.

Why is this statement true? I thought the rate of radioactive decay would be constant for an object?

Thanks!
.

Let's say the half-life for a particular substance is 2 years. Because nuclear decay exhibits 1st order kinetics, every 2 years ...the amount you had originally will cut in half.

So let's say you began with 100 grams of some sample. Originally you had 100%.

100% - Before any radioactive decay
50% remaining (50g) - after 1 half-life
25% remaining (25g) - after 2 half-life
12.5% remaining (12.5g) - after 3 half-life
6.25% remaining (6.25g) after 4 half-life

Between the 1st and 2nd half life - 25g decayed
Between the 2nd and 3rd half life - 12.5g decayed
Between the 3rd and 4th half life - 6.25g decayed

As you can see, that number is getting smaller and smaller with every half-life until all of the original sample is gone entirely. In other words, as an object gets "older," the the amount of decay per unit mass gets smaller.

 

[Rabolisk]

Constant rate would imply zero-order kinetics.

 

[Perkins]

Thanks for the explanations ilovemcat and Rabolisk! I understand the what the question is talking about now.

-- and thanks for writing out the example ilovemcat. That really helped!