Question

a) Define ‘disintegration constant’ and ‘mean life’ of a radioactive substance. Give the unit for each. b)Obtain the amount of 60Co27 necessary to provide a radioactive source of 8.0mCi strength. The half life of 60Co27 is 5.3 years.

Answer 1

Answer:

Disintegration Constant : is defined as change in number of atoms in a certain compound in unit time either normally or by certain physical or chemical process.It can be a fractional value or real number also, depending upon time for which change is considered.

It is represented by Lambda(λ).It's unit is Per second,Per hour ,Per days,Per month ,Per year.

Mean Life: Mean life of a particle is defined as total time taken by the particle to decay either half, one -fourth, two -third, etc.. of Original amount of that Particle.If the particle is reduced to half of original amount it is called half life. The unit of Mean life is , second, hour, months, years.

Mean life

     $=\frac{1}{\text{Decay Constant}}$

Half life of Co (27) =5.3 years

$Mean life = \frac{\text{half-life}}{ln(2)}=\frac{5.3}{0.693}=7.65$

$A_{t}=A_{0}e^{-kt}, where A_{t}, A_{0}$

are initial amount and final amount of an element or compound respectively.And k is decay constant.

Decay constant

     $=\frac{1}{7.65}=0.14$

$A_{t}=60, A_{0}=8,k=0.14$

Substituting these values in decay formula, and obtaining the time to reduce to 8.0 m Ci Strength

$60=8*e^{-0.14t}\\\\e^{-0.14 t}=7.5\\\\ e^{-0.14}*e^t=7.5\\\\0.869358*(2.72)^t=7.5\\\\(2.72)^t=8.62\\\\ t=2.15$

So, total time taken by the element to reduce from 60 mi to 8.0 mi is 2.15 second (approximately).

Answer 2

Answer:

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