Question

If you have 100 grams of a radioactive isotope with a half life of 10 years how much of the isotope will you have left after 10 years

Answer 1

Answer:

50.0 g.

Explanation:

• It is known that the decay of a radioactive isotope isotope obeys first order kinetics.

• Also, it is clear that in first order decay the half-life time is independent of the initial concentration.

• Half-life time is the time needed for the reactants to be in its half concentration.

• If reactant has initial concentration [A₀], after half-life time its concentration will be ([A₀]/2).

• So, the mentioned radioactive isotope after 10 years will have (100/2 = 50.0 g).

Thus, the amount of radioactive isotope is 50.0 g.

Answer 2

We want to find how much of a radioactive isotope we will have after a given time, given that we know the half life of the isotope.

After 10 years, there will be 50 grams of the isotope.

The half life of a given quantity is defined as the time such that the quantity is reduced ot its half.

So if we initially have a quantity A with a half time T, after the time T our quantity will be A/2.

Now we have 100 g of a radioactive isotope with a half life of 10 years. Then after that time, 10 years, we will have half that mass of isotopes.

This is 100g/2 = 50g

After 10 years we will have 50 grams of isotopes.

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