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Verified Answer :

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The correct answer is option C : 0.0625g of one gram of radium-226 will remain unchanged after four half-lives. 

Answer:

0.0625 g

Step-by-step explanation:

Given : The half-life of radium-226 is 1620 years.

Formula of half life:

\(P(t) =P_0(\frac{1}{2})^\frac{t}{1620}\)

So. \(P_0\) = initial amount

P(t)= mass of radioactive material at time interval (t)

1 half life = 1620 years

4 half lives = 4 1620

So, t = 4 1620

Substituting the values :

\(P(t) =1 (\frac{1}{2})^\frac{4\times 1620 }{1620}\)

\(P(t) = (\frac{1}{2})^4\)

\(P(t) = \frac{1}{16}\)

\(P(t) =0.0625\)

Hence  0.0625 g of one gram of radium-226 will remain unchanged after four half-lives

Option C is correct.