SATHEE: Modern Physics 3 Question 15

Modern Physics 3 Question 15

15. Two radioactive materials $X_{1}$ and $X_{2}$ 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 $X_{1}$ to that of $X_{2}$ will be $1 / e$ after a time

(a) $1 / 10 λ$

(b) $1 / 11 λ$

(c) $11 / 10 λ$

(d) $1 / 9 λ$

$(2000, 2 M)$

Show Answer

Solution:

$\frac{N_{x_{1}} (t)}{N_{x_{2}} (t)} = \frac{1}{e}$ or $\frac{N_{0} e^{- 10 λ t}}{N_{0} e^{- λ t}} = \frac{1}{e}$

(Initially, both have same number of nuclei say $N_{0}$ )

$\begin{aligned} or & e & = e^{- λ t} / e^{- 10 λ t} \\ or & e & = e^{9 λ t} \\ or & 9 λ t & = 1 \\ or & t & = \frac{1}{9 λ} \end{aligned}$

पिछला

अगला

गोपनीयता नीति

द्वारा संचालित Prutor@IITK

sathee@iitk.ac.in

SATHEE का मीडिया कवरेज

खेल स्टोर

ऐप स्टोर

Ask SATHEE

Welcome to SATHEE !
Select from 'Menu' to explore our services, or ask SATHEE to get started. Let's embark on this journey of growth together! 🌐📚🚀🎓

I'm relatively new and can sometimes make mistakes.
If you notice any error, such as an incorrect solution, please use the thumbs down icon to aid my learning.
To begin your journey now, click on "I understand".

Modern Physics 3 Question 15

15. Two radioactive materials X1 and X2 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 X1 to that of X2 will be 1/e after a time

Solution:

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

15. Two radioactive materials $X_{1}$ and $X_{2}$ 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 $X_{1}$ to that of $X_{2}$ will be $1 / e$ after a time