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PhysicsModern PhysicsRadioactivityEasy2 minPYQ_2020

PhysicsEasysingle choice

The activity of a sample of radioactive material is $A_{1}$ at time $t_{1}$ and $A_{2}$ at time $t_{2} (t_{2} > t_{1})$ . If its mean life is $T$ then which of the following is correct.

Options:

Answer:

Solution:

$A = A_{0} e^{- \frac{t}{T}}$
In time $t_{1}$ activity is $A_{1}$
$\Rightarrow A_{1} = A_{0} e^{- \frac{t_{1}}{T}}$ ....... (i)

In time $t_{2}$ activity is $A_{2}$
$\Rightarrow A_{2} = A_{0} e^{- \frac{t_{2}}{T}}$ ...... (ii)

Dividing equation (ii) by (i)
$\Rightarrow \frac{A_{2}}{A_{1}} = \frac{e^{- \frac{t_{2}}{T}}}{e^{- \frac{t_{1}}{T}}}$
$\Rightarrow A_{2} = A_{1} e^{- \frac{(t_{2} - t_{1})}{T}}$
$\Rightarrow A_{2} = A_{1} e^{\frac{(t_{1} - t_{2})}{T}}$

Stream:NTA_ABHYAS_NEETSubject:PhysicsTopic:Modern PhysicsSubtopic:Radioactivity

⏱ 2mℹ️ Source: PYQ_2020

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