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Nuclei

Question
CBSEENPH12047910

A block having 12g of element is placed in a room. This element is a radioactive element with half-life of 15 yr. After how many years will there be just 1.5 g of the element in the box?

  • 40 yr

  • 45 yr

  • 20 yr

  • 15 yr

Solution

B.

45 yr

Given:- T1/2 = 15 yr

           N0 = 12 g

          N = 1.5 g

∴           N = N0 e-λt

Where N is the number of radioactive nuclei at time t       

λ = radioactive decay constan or disintegration constant

⇒         e-λtNN0

Take log on both side

⇒          - λ t = ln NN0

⇒         t = 1λ ln N0N

⇒            = T120.693 ln N0N                        

Since      T12 = ln 2λ = 0.693λ                             

⇒            = 150.693 ln N0N

⇒         e-λt 150.93 × ln121.5

⇒          e-λt = 45 yr