SATHEE: nuclei Question 29

nuclei Question 29

Question: Q. 2. (i) State the law of radioactive decay. Write the SI unit of ‘activity’.

(ii) There are $4 \sqrt{2} \times 10^{6}$ radioactive nuclei in a given radioactive sample. If the halflife of the sample is $20 s$ , how many nuclei will decay in $10 s$ ?

$R$ A [Foreign I 2017]

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Solution:

Ans. (i) Statement : Rate of decay of a given radioactive sample is directly proportional to the total number of undecayed nuclei present in the sample

[Alternatively : $- \frac{d N}{d t} \propto N$ ]

Unit $\to$ becquerel (Bq)

(ii)

$N = N_{0} e^{- λ t}$

$\frac{N}{N_{0}} = {(\frac{1}{2})}^{n}$

$\begin{aligned} n & = \frac{t}{T_{1 / 2}} = \frac{10}{20} = \frac{1}{2} \Rightarrow N & = 4 \sqrt{2} \times 10^{6} \times {(\frac{1}{2})}^{1 / 2} & = \sqrt{2} \times 10^{6} nuclei \end{aligned}$

[CBSE Marking Scheme 2017]

Detailed Answer :

For solving numerical (part-ii), kindly refer to Q. 1 (ii) Short Answer Type Questions-II of Topic-I of this chapter.

Nuclei

nuclei Question 29

Detailed Answer :

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Nuclei

nuclei Question 29

Detailed Answer :

Table of Contents

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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