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The half life of radioactive substance is 1620 years and 405 years for \alpha emission and    \beta  emission respectively. Time (in years) during which half of sample will decay if both \alpha  and  \beta emission is simultaneous is:

Option: 1

324


Option: 2

405


Option: 3

1620


Option: 4

2025


Answers (1)

best_answer

As we learn

Simultaneous decay -

\lambda _{eff}= \lambda _{1}+\lambda _{2}+....\lambda _{n}

- wherein

Effective decay constant is when a nuclei decay in to more than one product at one time.

 

 \lambda =\lambda _{1}+\lambda _{2}=\frac{0.693}{T}=\frac{0.693}{T_{1}}+\frac{0.693}{T_{2}}

\frac{1}{T}=\frac{1}{T_{1}}+\frac{1}{T_{2}}

OR            \frac{1}{T}=\frac{1}{1620}+\frac{1}{405}

\frac{1}{T}=\frac{5}{1620}

OR T=324 years

 

Posted by

Ritika Kankaria

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