The weight based ratio of $U^{238}$ and $P b^{226}$ in a sample of rock in $4 : 3$ . If the half life of $U^{238}$ is $4.5 \times 10^{9}$ years then the age of rock is

9.0 \times 10^{9}

years

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6.3 \times 10^{9}

years

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4.5 \times 10^{9}

years

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3.78 \times 10^{9}

years

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Solution

The correct option is D $3.78 \times 10^{9}$ years
Let the total amount of $U^{238}$ in beginning be $7$ units. So out of $7$ units, $3$ has decayed to the $P b^{226}$ .
Half-life is $4.5 \times 10^{9}$ .
So age of rock is $4.5 \times 10^{9} \times \frac{{log}_{e} \frac{7}{4}}{{log}_{e} 2} = 3.63 \times 10^{9} / y e a r s$

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The weight based ratio of U238 and Pb226 in a sample of rock in 4:3. If the half life of U238 is 4.5×109 years then the age of rock is

The correct option is D 3.78×109 yearsLet the total amount of U238 in beginning be 7 units. So out of 7 units, 3 has decayed to the Pb226.Half-life is 4.5×109.So age of rock is 4.5×109×loge74loge2=3.63×109/years

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