The half life period of a radioactive element X is same as the mean life time of another radioactive element Y. Initially they have the same number of atoms. Then
X and Y decay the same rate always
X and Y have same decay rate initially
X will decay faster than Y
Y will decay faster than X
A
X will decay faster than Y
B
Y will decay faster than X
C
X and Y have same decay rate initially
D
X and Y decay the same rate always
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Solution
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The correct option is BX will decay faster than Y Let the number of atoms of X and Y presented initially be No.
Number of atoms of X remaining after time t is given by NX=Noe−λt
NX=Noe−ln2tT1/2=Noe−ln2tTm (∵T1/2=Tm)
where and T1/2 is the half-time of X ans Tm is the mean life time of Y.
Number of atoms of Y remaining after time t is given by NY=Noe−λt=Noe−tTm
⟹NX<NY at any time t
Thus, X decays faster than Y.
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