GATE-2007
63.After
decaying through 7 half-life periods , the original amount of
radioactive substance that reduces to an amount of 1/64g is,
A)
0.25 g B) 0.50 g C) 1.0g D)
2.0g
Solution:
If
‘N’ is the amount of substance remained after ‘t’ half lifes
of a substance N0 are related by,
\frac{N}{N_{0}}=(\frac{1}{2})^{\frac{t}{t_{\frac{1}{2}}}}--(1)
t =7t_{\frac{1}{2}}
N =\frac{1}{64}
N_{0}=?
Substitute the above values in the eq(1)
\frac{1}{64_{N_{0}}}=\frac{1}{2}^{\frac{7t_{\frac{1}{2}}}{t\frac{1}{2}}}
\frac{1}{64N_{0}}=2^{-7}
2^{7}=64N_{0}
N_{0}=\frac{2^{7}}{2^{6}}
N_{0}=2^{7-6}
N_{0}=2grams
If P is the amount of substance remained after 'n' half lifes of a substance Po are related by P=Po/2^n
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