Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  •  A small quantity of solution containing the radionuclide  (Half life 15 hours), of activity 1.0 microcurie,

 A small quantity of solution containing the radionuclide \mathrm{Na}^{24} (Half life 15 hours), of activity 1.0 microcurie, is injected into the blood of a patient. A sample of the blood of volume 1 \mathrm{~cm}^3 taken after 5 hours shows an activity of 296 disintegrations per minute. The total volume of blood in the patients body ( 1 \mathrm{Ci}=3.7 \times 10^{10}. disintegrations per second)
 

Option: 1

5.9 I
 


Option: 2

4.6 I

 


Option: 3

6.8 I
 


Option: 4

2.5 I


Answers (1)

best_answer

The activity varies according to the equation,

A(t)=A_0 e^{-\lambda t}
or, \mathrm{A}(\mathrm{t})=\mathrm{A}_0\left(\frac{1}{2}\right)^{t / T_{1 / 2}}

In the problem, 

A(t=5 \mathrm{hr})=296 \mathrm{~disintegrations }/ \mathrm{min},
\begin{aligned} & \frac{296}{60}=\mathrm{A}_0\left(\frac{1}{2}\right)^{5 / 15} \\ & \text { or, } \mathrm{A}_0=\frac{296}{60} \times 2^{1 / 3}=6.22 \text { disintegration } / \mathrm{sec} \text {. } \\ \end{aligned}The initial activity of 1 cc of blood

If the total volume of blood is V cc

 \begin{aligned} & 6.22 \mathrm{~V}=3.7 \times 10^{10} \times 10^{-6}=5948 \mathrm{cc} \\ & \Rightarrow \mathrm{V}=5.9 \ell \text {. } \\ \end{aligned}
 

 

Posted by

Anam Khan

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Latest Question