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Wave Optics

Question
CBSEENPH12038719
Wired Faculty App

State the laws of radioactivity.
A radioactive substance has a half-life period of 30 days. Calculate (i) time taken for 34 of original number of atoms to disintegrate and (ii) time taken for 18 of the original number of atoms to remain unchanged.

Solution
In any radioactive sample, undergoing α, β or γdecay, the number of nucleii undergoing decay per unit time is directly proportional to the total number of nuclei in the sample. This is known as the radioactive decay law. 

Let, N be the number of nucleii in the sample, 
∆N is the sample undergoing decay and, 
∆t  is the time then, 

                            ∆N∆t ∝ N 

⇒                        ∆N∆t= λN 

where, λ is the decay constant. 


Numerical: 

Half -period of radioactive substance = 30 days
Number of atoms disintegrated = 34  N0
Number of atoms left after time t,  N = N0 - 34N0 = 14N0 

Number of half lives in time t days,
                                    
                        n = tT = t30
where, 

T = Half life time
n = no. of half lives
t = time for disintegrates 

Number of nuclei left after n half lives is given by, 

                      N = N012N 
Therefore, 
                    N04 = N012t/30  

⇒            (2)t/30 = 4 = (2)2

⇒               t30 = 2  or  t = 60 days

(ii) Now, using the formula,  N = N012n

∴                    N08 = N012t/30

⇒               (2)t/30 = 8 = (2)3      
      
⇒                  t30 = 3
i.e.,                      t = 90 days, is the time taken for 1/8 of the original number of atoms to remain unchanged.

                                        
                                    

 

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