(D) Given: Half-life $(t_{1/2})$ = $5 \, \text{years}$,Total time $(t)$ = $15 \, \text{years}$,Initial amount $(N_0)$ = $64 \, \text{g}$.Number of hal

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(D) Given: Half-life $(t_{1/2})$ = $5 \, \text{years}$,Total time $(t)$ = $15 \, \text{years}$,Initial amount $(N_0)$ = $64 \, \text{g}$.Number of half-lives $(n)$ = $\frac{t}{t_{1/2}} = \frac{15}{5} = 3$.The amount remaining $(N)$ is given by the formula: $N = \frac{N_0}{2^n}$.Substituting the values: $N = \frac{64}{2^3} = \frac{64}{8} = 8 \, \text{g}$.Therefore,the correct option is $(D)$.

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

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If the half-life of a substance is $5 \, \text{years}$,then the total amount of substance left after $15 \, \text{years}$,when the initial amount is $64 \, \text{grams}$,is ....... $\text{gm}$.

AIEEE 2002 All AIEEE

A
$16$
B
$2$
C
$32$
D
$8$

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If the half-life of a substance is $5 \, \text{years}$,then the total amount of substance left after $15 \, \text{years}$,when the initial amount is $64 \, \text{grams}$,is ....... $\text{gm}$.

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