The half-life of a radioactive element is 10 minutes. If the initial count rate is 368 counts per minute, find the time by which, the count rate would reach 23 counts per minute. Ans. (40 minutes)



Data Given:


Half-life of radioactive element = T₁/₂ = 10 min 
Initial count rate = 368 counts per minute
Final count rate = 368 counts per minute


To Find:


Time taken = t = ?


Solution:

Initial count rate = 368 counts per minute

Count decrease during first half-life (1 T₁/₂) = 368 ÷ 2 = 184 count per minutes

Count decrease during 2nd half-life (3 T₁/₂) = 184 ÷ 2 = 92 count per minutes

Count decrease during 3rd half-life (4 T₁/₂) = 92 ÷ 2 = 46 count per minutes

Count decrease during 4th half-life (4 T₁/₂) = 46 ÷ 2 = 23 count per minutes

thus, the count rate decreases from 368 count per minute to 23 counts per minute, Four half-lives (4 T₁/₂) are elapsed. therefore, using the formula

Time = Number of Half-lives ï½˜ half-life ( T₁/₂ )

by putting values

Time = 4 ï½˜ 10 minutes 

Time = 40 minutes   -----Ans