A solution containing active cobalt Co 2760 having an activity of 0.8 μ Ci and decay constant λ is injected in an animal's body. When 1cm^ 3 blood is drawn from the animal's body after 10h of injection, the activity was

Correct answer: C. 5L Let total volume of blood is v , initial activity A _ 0 = 0 . Qμ C _ i its activity at time t A = A _ o e^ - activity of x volume A^ 1 = ((A)/(V))X = X ( A _ o V ) e^ - V = X ( A _ 0 A^ 1 ) e^ - V = (1cm^ 3 )( 8 × 10 ^ - 7 × 3.7 × 10 ^ 10 (300)/(60) )(0.84) = 4.97 × 10 ^ 3 cm^ 2 = 4.97 litre &

NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Physics
Chapter: Nuclear Physics

NTA Abhyas 2020 · Physics · Nuclear Physics

A solution containing active cobalt Co 2760 having an activity of...

A solution containing active cobalt

Co 2760

having an activity of

0.8 \mu Ci

and decay constant

\lambda

is injected in an animal's body. When

1cm^{3}

blood is drawn from the animal's body after

10h

of injection, the activity was found to be

300dpm

(decays per minute), then the total volume of blood in the animal's body is close to

[ 1Ci = 3.7 \times {10}^{10}dps

(decays per second) and at

t = 10h

the value of

e^{- \lambdat} = 0.84 ]

Options

A $4L$
B $6L$
C $5L$
D $7L$

Correct answer

C. $5L$

Step-by-step solution

Let total volume of blood is

\text{v}

, initial activity

{A}_{0} = 0 . Q\mu{C}_{i}

its activity at time

\text{t}

A = {A}_{o} e^{- \lambdat}

activity of

\text{x}

volume

A^{1} = \left(\dfrac{A}{V}\right)X = X

\left(\dfrac{{A}_{o}}{V}\right) e^{- \lambdat}

<br /><br />

V = X \left(\dfrac{{A}_{0}}{A^{1}}\right)

e^{- \lambdat}

V = \left(1cm^{3}\right)\left(\dfrac{8 \times {10}^{- 7} \times 3.7 \times {10}^{10}}{\dfrac{300}{60}}\right)\left(0.84\right)

= 4.97 \times {10}^{3}cm^{2} = 4.97

litre
&

Practice Nuclear Physics on Quantrex Academy →

More from Nuclear Physics

A nuclear reactor starts producing a radioactive nuclide X from t = 0 , at a constant… JEE Advanced 2026 Two radioactive substances A and B of mass numbers 200 and 212 respectively, shows… JEE Main 2026 The energy released if hydrogen atoms are combined to form ^ 4 _ 2 He is __________ MeV.… JEE Main 2026 The energy released when (7)/(17.13) kg of ^ 7 _ 3 Li is converted into ^ 4 _ 2 He by… JEE Main 2026 Assuming the experimental mass of ^ 12 _ 6 C as 12 u , the mass defect of ^ 12 _ 6 C atom… JEE Main 2026 Two nuclei of mass number 3 combine with another nucleus of mass number 4 to yield a… JEE Main 2026 The binding energy per nucleon of ^ 209 _ 83 Bi is _______ MeV. [Take m(^ 209 _ 83 Bi) =… JEE Main 2026 A nucleus has mass number α and radius R_ α . Another nucleus has mass number β and… JEE Main 2026 Full Nuclear Physics list All NTA Abhyas JEE Main PYQs