SATHEE: Nuclei - Result Question 71

Nuclei - Result Question 71

72. The decay constant of a radio isotope is $λ$ . If $A_{1}$ and $A_{2}$ are its activities at times $t_{1}$ and $t_{2}$ respectively, the number of nuclei which have decayed during the time $(t_{1} - t_{2})$ :

[2010]

(a) $λ (A_{1} - A_{2})$

(b) $A_{1} t_{1} - A_{2} t_{2}$

(d) $(A_{1} - A_{2}) / λ$

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Answer:

Correct Answer: 72. (d)

Solution:

(d) Activity is given by

$A = \frac{d N}{d t} = - λ N$

Activity at time $t_{1}$ is

$A_{1} = - λ N_{1}$

and activity at time $t_{2}$ is $A_{2} = - 1 N_{2}$ As $t_{1} > t_{2}$ , therefore, number of atoms remained after time $t_{1}$ is less than that remained after time $t_{2}$ . That is, $N_{1} < N_{2}$ .

$∴$ number of nuclei decayed in $(t_{1} - t_{2})$

$= N_{2} - N_{1} = \frac{(A_{1} - A_{2})}{λ}$

If a radioactive element $A$ disintegrates to form another radioactive element $B$ , which inturn disintegrates to form another element $C$ ,

Rate of disintegration of $A = \frac{d N_{1}}{d t} = - λ_{1} N_{1}$

Rate of disintegration of $B = \frac{d N_{2}}{d t} = - λ_{2} N_{2}$

Net rate of formation of $B =$ Rate of disintegration of A - Rate of disiutegration of $B = λ_{1} N_{1} - λ_{2} N_{2}$

Nuclei - Result Question 71

72. The decay constant of a radio isotope is $λ$ . If $A_{1}$ and $A_{2}$ are its activities at times $t_{1}$ and $t_{2}$ respectively, the number of nuclei which have decayed during the time $(t_{1} - t_{2})$ :

Answer:

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Nuclei - Result Question 71

72. The decay constant of a radio isotope is λ. If A1 and A2 are its activities at times t1 and t2 respectively, the number of nuclei which have decayed during the time (t1−t2) :

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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72. The decay constant of a radio isotope is $λ$ . If $A_{1}$ and $A_{2}$ are its activities at times $t_{1}$ and $t_{2}$ respectively, the number of nuclei which have decayed during the time $(t_{1} - t_{2})$ :