(A) The number of half-lives $(n)$ is calculated as $n = \frac{\text{Total time}}{\text{Half-life}} = \frac{16 \ h}{4 \ h} = 4$.Remaining mass $(N_t)$

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(A) The number of half-lives $(n)$ is calculated as $n = \frac{\text{Total time}}{\text{Half-life}} = \frac{16 \ h}{4 \ h} = 4$.Remaining mass $(N_t)$ is given by the formula $N_t = N_0 \times (\frac{1}{2})^n$,where $N_0 = 200 \ g$.$N_t = 200 \times (\frac{1}{2})^4 = 200 \times \frac{1}{16} = 12.5 \ g$.The disintegrated amount is the initial mass minus the remaining mass: $\text{Disintegrated amount} = N_0 - N_t = 200 \ g - 12.5 \ g = 187.5 \ g$.

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

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The half-life of a radioactive isotope is $4 \ hours$. If the initial mass of the isotope is $200 \ g$,then what will be the disintegrated amount of it after $16 \ hours$?

A
$187.5$
B
$12.5$
C
$25$
D
$175$

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Rate of decay and Half-life

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The half-life of a radioactive isotope is $4 \ hours$. If the initial mass of the isotope is $200 \ g$,then what will be the disintegrated amount of it after $16 \ hours$?

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The half-life period of a radioactive element is $30 \ min$. One sixteenth of the original quantity of the element will remain unchanged after ........... $min$.

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