Home
Class 12
PHYSICS
Obtain the amount of ""(27)^(60)Co neces...

Obtain the amount of `""_(27)^(60)Co` necessary to provide a radioactive source of 8.0 mCi strength. The half-life of `""_(27)^(60)Co` is 5.3 years.

Text Solution

Verified by Experts

Strength of radioactive source
= 8.0 mCi = `8.0xx10^(-3)`Ci
= `8.0xx10^(-3)xx3.7xx10^(10)` disintegrations `s^(-1)`
Since the strength of the source decreases with time,
`therefore(dN)/(dt)=-29.6xx10^(7)`
But `(dN)/(dt)=-lamdaN`
`therefore" "=-lamdaN=-29.6xx10^(7)`
or `lamdaN=-29.6xx10^(7)orN=(29.6xx10^(7))/lamda`
or `N=(29.6xx10^(7)xxT)/0.693`
Promotional Banner

Similar Questions

Explore conceptually related problems

Radioactive ""_(27)^(60)Co is transformed into stable ""_28^60Ni by emitting two gamma - rays of energies

The count rate of nuclear radiation coming from a radioactive sample containing I^128 varies with time as follows. Time t (minute): 0 25 50 75 100 Count rate R(10^9 s^(-1)) : 30 16 8.0 3.8 2.0 (a) plot In (R_0//R) against t. (b) From the slope of the best straight line through the points,Find the decay constant lambda .(c ) Calculate the half-life t_(1//2) .

A radioactive sample contains 10^(-3) kg each of two species A and B with half-life 4 days and 8 days respectively. The ratio of the amounts of A and B after a periof of 16 days is

Obtain the resonant frequency and Q-factor of a series LCR circuit with L = 3.0 H, C = 27 muF , and R= 7.4Omega . It is desired to improve the sharpness of the resonance of the circuit by reducing its 'full width at half maximum' by a factor of 2. Suggest a suitable way.

Natural water contains a small amount of tritium (H_1^3) . This isotope beta -decays with a half-life of 12.5 years.A mountaineer while climbing towards a difficult peak finds debris of some earlier unsuccessful attempt.Among other things he finds a sealed bottle of whisky.On returm he analyses the whisky and finds that it contains only 1.5 per cent of hte H_1^3 radioactivity as compared to a recently purchased bottle marked '8 years old' .Estimate the time of that unsuccessful attempt.

Co^57 decays to Fe^57 by beta^+ -emission.The resulting Fe^57 is in its excited state and comes to the ground state by emitting gamma -rays.The half-life of beta^+ -decay is 270 days and that of the gamma -emission is 10^(-8) s.A sample of Co^57 given 5.0xx10^9 gamma rays per second.How much time will elapse before the emission rate of gamma rays drops to 2.5xx10^9 per second ?

ltimg src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/CEN_ALG_DPP_4_2_E01_231_Q01.png" width="80%"gt Let ABCD is a unit square and each side of the square is divided in the ratio alpha : (1-alpha) (0 lt alpha lt 1) . These points are connected to obtain another square. The sides of new square are divided in the ratio alpha : (1-alpha) and points are joined to obtain another square. The process is continued idefinitely. Let a_(n) denote the length of side and A_(n) the area of the n^(th) square If alpha=(1)/(3) , then the least value of n for which A_(n) lt (1)/(10) is