Aradioactive isotope has a half-life of 10 years. what fraction of the original mass will remain unchanged after 50 years

The fraction of the original mass of the radioactive isotope with a half-life of 10 years that will remain after 50 years is 1/32.

We can find the fraction of the original mass with the exponential decay equation:

 (1)

Where:

N(t): is the amount of radioactive isotope at time t

N₀: is the initial amount of radioactive isotope

λ: is the decay constant

t: is the time = 50 y

We can find the decay constant as follows:

  (2)

Where:

: is the half-life of the isotope = 10 y

The decay constant is (eq 2):

Now, the fraction of the original amount is (eq 1):

Since we need to calculate the fraction of the original mass, after some algebraic operations we have:

Therefore, the fraction of the original mass that will remain is 1/32.

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The fraction is calculated like this:

If you want an universal equation for all problems like this:

the correct answer would be d. hope this !

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