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Byju's Answer

Standard XII

Physics

Law of Radioactivity

To determine ...

Question

To determine the half life of a radioactive element, a student plots a graph of $l n | \frac{d N (t)}{d t} |$ versus $t$ . Here $\frac{d N (t)}{d t}$ is the rate of radioactive decay at time $t$ . If the number of radioactive nuclei of this element decreases by a factor ofp after 4.16 years, the value of $p$ is:

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Solution

The correct option is D $8$
$N = N_{0} e^{- λ t}$

$l n | \frac{d N}{d t} | = l n (N_{0} λ) - λ t$
From graph, $λ = \frac{1}{2}$ per year
$t_{1 / 2} = \frac{0.693}{1 / 2} = 1.386$ year
$4.16 y r s = 3 t_{1 / 2}$
$∴ p = 8$

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To determine the half life of a radioactive element, a student plots a graph of ln|dN(t)dt| versus t. Here dN(t)dt is the rate of radioactive decay at time t. If the number of radioactive nuclei of this element decreases by a factor ofp after 4.16 years, the value of p is:

The correct option is D 8N=N0e−λtln|dNdt|=ln(N0λ)−λtFrom graph, λ=12 per year t1/2=0.6931/2=1.386 year4.16yrs=3t1/2∴p=8

The correct option is D $8$
$N = N_{0} e^{- λ t}$

$l n | \frac{d N}{d t} | = l n (N_{0} λ) - λ t$
From graph, $λ = \frac{1}{2}$ per year
$t_{1 / 2} = \frac{0.693}{1 / 2} = 1.386$ year
$4.16 y r s = 3 t_{1 / 2}$
$∴ p = 8$