SATHEE: Modern Physics 3 Question 4

Modern Physics 3 Question 4

4. A sample of radioactive material $A$ , that has an activity of 10 $m C i (1 C i = 3.7 \times 10^{10}$ decays/s) has twice the number of nuclei as another sample of a different radioactive material $B$ which has an activity of $20 m C i$ . The correct choices for half-lives of $A$ and $B$ would, then be respectively

(Main 2019, 9 Jan I)

(a) 20 days and 10 days

(b) 5 days and 10 days

(d) 20 days and 5 days

Show Answer

Solution:

Activity of a radioactive material is given as

$R = λ N$

where, $λ$ is the decay constant and $N$ is the number of nuclei in the radioactive material.

For substance $A$ ,

$R_{A} = λ_{A} N_{A} = 10 m C i$

For substance $B$ ,

$R_{B} = λ_{B} N_{B} = 20 m C i$

As given in the question,

$N_{A} = 2 N_{B}$

$\Rightarrow R_{A} = λ_{A} (2 N_{B}) = 10 m C i$

$∴$ Dividing Eq. (ii) and Eq.(i), we get

$\frac{R_{A}}{R_{B}} = \frac{λ_{A} (2 N_{B})}{λ_{B} (N_{B})} = \frac{10}{20}$

or $\frac{λ_{A}}{λ_{B}} = \frac{1}{4}$

As, half-life of a radioactive material is given as

$T_{1 / 2} = \frac{0.693}{λ}$

$∴$ For material $A$ and $B$ , we can write

$\frac{{(T_{1 / 2})}_{A}}{{(T_{1 / 2})}_{B}} = \frac{\frac{0.693}{λ_{A}}}{\frac{0.693}{λ_{B}}} = \frac{λ_{B}}{λ_{A}}$

Using Eq. (iii), we get

$\frac{{(T_{1 / 2})}_{A}}{{(T_{1 / 2})}_{B}} = \frac{4}{1}$

Hence, from the given options, only option (d) satisfies this ratio.

Therefore, ${(T_{1 / 2})}_{A} = 20$ days

and ${(T_{1 / 2})}_{B} = 5$ days

पिछला

अगला

Modern Physics 3 Question 4

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

Modern Physics 3 Question 4

4. A sample of radioactive material A, that has an activity of 10 mCi(1Ci=3.7×1010 decays/s) has twice the number of nuclei as another sample of a different radioactive material B which has an activity of 20mCi. The correct choices for half-lives of A and B would, then be respectively

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