Nucleus - 6

(2) A small Quantity of solution containing Na-24 radioactive nuclei
t_1/2 = 15h of activity 1.0 ci is injected into the blood of a person. A sample of blood of volume 1cm³ taken after 5th, throws an activiy of 296 d/ min.
Determine the total voume of blood in the body of person
Let volume of blood be V
activity of 1 cm³ initially =
activity after 5 hrs = A¹ = = 4.93 dps




(3) Polinum is used forgeneration of electricity, assuming the efficiency of the electricity, assuming the efficiency of the electric machine to be 10% how much P₀ is required 693 days. Also find the intial activity of material.
(mass of nucleii P₀ - 210 = 209.98264 u Ph - 206 = 205.97440 u ₂He⁴ = 4.00260 u)
mass defect = (209.98264) - (205.97440 + 4.00260) = 000564u = 5.64 x 10^-3 x 931Mev = 8.34 x 10^-3J.
No. of fissions required for 1.2 x 10⁷J = = 1.43 x 10¹⁹
Since efficiency of machine is 10%
Actually no. of fissions occuring = 1.43 x 10¹⁹ x 10 = 1.43 x 10²⁰
mass of polinium required = x 210 = 0.0485g
at the end of 693days 0.0483g of P₀ must be present
693 days = 138.6 x 5 = 5 x t_1/2
intial mass of polinium = 0.0483 x 2⁵ = 0.0483 x 32 = 1.5456g
intial activity =…N₀=…..X 1.43 x 10²⁰ x 32
= 2.2 x 10¹⁹/day

Hard:

1. Nuclei of a radio active element A are being produced at a constant rate . The element has a decay constant . At time t = 0, there are N₀ nuclei of the element.
   (a) Calculate the number No of Nuclei of A at time t.
   (b) If after half life of a , and also the limiting value of Nas t
   Solution:- Rate of production =
   rate of decay = [n]
   integrating
   
   
   (Ans to (a) part)
   
   at t =
   
   limiting value i.e. as t