The radium and uranium atoms in a sample of u | vedclass

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(C) In radioactive equilibrium,the rate of decay of the parent is equal to the rate of decay of the daughter: $\lambda_R N_R = \lambda_U N_U$.Since $\

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$4.53 	imes 10^9$ years

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(C) In radioactive equilibrium,the rate of decay of the parent is equal to the rate of decay of the daughter: $\lambda_R N_R = \lambda_U N_U$.Since $\lambda = \frac{0.693}{t_{1/2}}$,we have $\frac{0.693}{t_{1/2}(R)} 	imes N_R = \frac{0.693}{t_{1/2}(U)} 	imes N_U$.This simplifies to $\frac{N_R}{N_U} = \frac{t_{1/2}(R)}{t_{1/2}(U)}$.Given $\frac{N_R}{N_U} = \frac{1}{2.8 	imes 10^6}$ and $t_{1/2}(R) = 1620$ years.Substituting the values: $\frac{1}{2.8 	imes 10^6} = \frac{1620}{t_{1/2}(U)}$.Therefore,$t_{1/2}(U) = 1620 	imes 2.8 	imes 10^6 = 4536 	imes 10^6 = 4.536 	imes 10^9$ years.Rounding to the nearest option,the answer is $4.53 	imes 10^9$ years.

The radium and uranium atoms in a sample of uranium mineral are in the ratio of $1 : 2.8 \times 10^6$. If the half-life period of radium is $1620$ years,the half-life period of uranium will be:

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