SATHEE: Modern Physics 5 Question 3

Modern Physics 5 Question 3

3. Two radioactive materials $A$ and $B$ have decay constants $10 λ$ and $λ$ , respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of $A$ to that of $B$ will be $1 / e$ after a time

(a) $\frac{1}{11 λ}$

(b) $\frac{11}{10 λ}$

(d) $\frac{1}{10 λ}$

Show Answer

Answer:

Correct Answer: 3. (c)

Solution:

Given, $λ_{A} = 10 λ$ and $λ_{B} = λ$

Number of nuclei (at any instant) present in material is

$N = N_{0} e^{- λ t}$

So, for materials $A$ and $B$ , we can write

$\frac{N_{A}}{N_{B}} = \frac{e^{- λ_{A} t}}{e^{- λ_{B} t}} = e^{- (λ_{A} - λ_{B}) t}$

Given,

$\frac{N_{A}}{N_{B}} = \frac{1}{e}$

Equating Eqs. (i) and (ii), we get

$\begin{aligned} \frac{1}{e} & = e^{- (λ_{A} - λ_{B}) t} \\ \Rightarrow e^{- 1} & = e^{- (λ_{A} - λ_{B}) t} \end{aligned}$

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

$\begin{array}{ll} or & (λ_{A} - λ_{B}) t = 1 \\ \Rightarrow & t = \frac{1}{λ_{A} - λ_{B}} \end{array}$

By putting values of $λ_{A}$ and $λ_{B}$ in the above equation, we get

$t = \frac{1}{10 λ - λ} \Rightarrow t = \frac{1}{9 λ}$

पिछला

अगला

Modern Physics 5 Question 3

3. Two radioactive materials $A$ and $B$ have decay constants $10 λ$ and $λ$ , respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of $A$ to that of $B$ will be $1 / e$ after a time

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

Modern Physics 5 Question 3

3. Two radioactive materials A and B have decay constants 10λ and λ, respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of A to that of B will be 1/e after a time

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

Menu

3. Two radioactive materials $A$ and $B$ have decay constants $10 λ$ and $λ$ , respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of $A$ to that of $B$ will be $1 / e$ after a time