(B) Let the initial number of uranium atoms be $N_0$. Since the rock contains an equal number of uranium and lead atoms,the number of uranium atoms re

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(B) Let the initial number of uranium atoms be $N_0$. Since the rock contains an equal number of uranium and lead atoms,the number of uranium atoms remaining $(N)$ is half of the initial number,i.e.,$N = \frac{N_0}{2}$. This implies that one half-life has passed. The age of the rock $(t)$ is equal to the half-life $(t_{1/2})$ of uranium. Therefore,$t = 4.5 \times 10^9$ years.

Class 12 Chemistry Nuclear Chemistry Rate of decay and Half-life

Medium

$A$ sample of rock from the moon contains an equal number of atoms of uranium and lead ($t_{1/2}$ for $U = 4.5 \times 10^9$ years). The age of the rock would be:

A
$9.0 \times 10^9$ years
B
$4.5 \times 10^9$ years
C
$13.5 \times 10^9$ years
D
$2.25 \times 10^9$ years

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Nuclear Chemistry

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Rate of decay and Half-life

$A$ piece of wood was found to have the $C^{14}/C^{12}$ ratio $0.7$ times that in a living plant. The time period when the plant died is ....... $years$ (Half-life of $C^{14} = 5760 \, yrs$).

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$_{11}Na^{24}$ has a half-life of $15 \ h$. On heating,its half-life will:

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$8 \ g$ of a radioactive substance is reduced to $0.5 \ g$ after $1 \ hour$. The ${t_{1/2}}$ of the radioactive substance is ......... $\min$.

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Radioactive lead $_{82}Pb^{201}$ has a half-life of $8 \ hours$. Starting from $1 \ mg$ of this isotope,how much will remain after $24 \ hours$?

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The half-life of $1 \ g$ of a radioactive sample is $9 \ hours$. The radioactive decay obeys first-order kinetics. The time required for the original sample to reduce to $0.2 \ g$ is .......... $hours$.

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$A$ sample of rock from the moon contains an equal number of atoms of uranium and lead ($t_{1/2}$ for $U = 4.5 \times 10^9$ years). The age of the rock would be:

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$A$ piece of wood was found to have the $C^{14}/C^{12}$ ratio $0.7$ times that in a living plant. The time period when the plant died is ....... $years$ (Half-life of $C^{14} = 5760 \, yrs$).

$_{11}Na^{24}$ has a half-life of $15 \ h$. On heating,its half-life will:

$8 \ g$ of a radioactive substance is reduced to $0.5 \ g$ after $1 \ hour$. The ${t_{1/2}}$ of the radioactive substance is ......... $\min$.

Radioactive lead $_{82}Pb^{201}$ has a half-life of $8 \ hours$. Starting from $1 \ mg$ of this isotope,how much will remain after $24 \ hours$?

The half-life of $1 \ g$ of a radioactive sample is $9 \ hours$. The radioactive decay obeys first-order kinetics. The time required for the original sample to reduce to $0.2 \ g$ is .......... $hours$.

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