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Nuclei

Question
CBSEENPH12039626

The half-life period of a radio-active element X is same as the mean life-time of another radio-active element Y. Initially, they have the same number of atoms. Then

  • X will decay faster than Y

  • Y will decay faster than X

  • X and Y have same decay rate initially

  • X and Y decay at same rate always

Solution

B.

Y will decay faster than X

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straight tau subscript mean space equals 1 over straight lambda subscript straight y semicolon space dN over dt space equals space minus space λN
fraction numerator In 2 over denominator straight lambda subscript straight x end fraction space equals space 1 over straight lambda subscript straight y space
rightwards double arrow space straight lambda subscript straight x space equals space straight lambda subscript straight y space left parenthesis 0.6932 right parenthesis
rightwards double arrow space straight lambda subscript straight y space greater than space straight lambda subscript straight x