SATHEE: Modern Physics 5 Question 2

Modern Physics 5 Question 2

2. Two radioactive substances $A$ and $B$ have decay constants $5 λ$ and $λ$ , respectively. At $t = 0$ , a sample has the same number of the two nuclei. The time taken for the ratio of the number of nuclei to become ${\frac{1}{e}}^{2}$ will be

(Main 2019, 10 April II)

(a) $2 / λ$

(b) $1 / 2 λ$

(d) $1 / λ$

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Answer:

Correct Answer: 2. (b)

Solution:

Number of active nuclei remained after time $t$ in a sample of radioactive substance is given by

$N = N_{0} e^{- λ t}$

where, $N_{0} =$ initial number of nuclei at $t = 0$ and $λ =$ decay constant.

Here, at $t = 0$ ,

Number of nuclei in sample $A$ and $B$ are equal, i.e.

Also,

$N_{0_{A}} = N_{0_{B}} = N_{0}$

So, after time $t$ , number of active nuclei of $A$ and $B$ are

$N_{A} = N_{0} e^{- 5 λ t} and N_{B} = N_{0} e^{- λ t}$

If $\frac{N_{A}}{N_{B}} = \frac{1}{e^{2}}$ , then

$\frac{N_{A}}{N_{B}} = \frac{N_{0} e^{- 5 λ t}}{N_{0} e^{- λ t}} = \frac{1}{e^{2}} \Rightarrow e^{(λ - 5 λ) t} = e^{- 2}$

Comparing the power of $e$ on both sides, we get

$\begin{aligned} 4 λ t & = 2 \\ \Rightarrow t & = \frac{1}{2 λ} \end{aligned}$

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Modern Physics 5 Question 2

2. Two radioactive substances $A$ and $B$ have decay constants $5 λ$ and $λ$ , respectively. At $t = 0$ , a sample has the same number of the two nuclei. The time taken for the ratio of the number of nuclei to become ${\frac{1}{e}}^{2}$ will be

Answer:

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Modern Physics 5 Question 2

2. Two radioactive substances A and B have decay constants 5λ and λ, respectively. At t=0, a sample has the same number of the two nuclei. The time taken for the ratio of the number of nuclei to become 1e2 will be

Answer:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

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2. Two radioactive substances $A$ and $B$ have decay constants $5 λ$ and $λ$ , respectively. At $t = 0$ , a sample has the same number of the two nuclei. The time taken for the ratio of the number of nuclei to become ${\frac{1}{e}}^{2}$ will be