Q. The half life of _{92}U^{238}undergoing α-decay is 4.5 × 10^{9} Its activity of 1g sample is

(a) 1.23 × 10^{4} Bq

(b) 2.4 × 10^{5} Bq

(c) 1.82 × 10^{6} Bq

(d) 4.02 ×10^{8} Bq

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Ans: (a)

Sol: Half life , T

_{1/2}= 4.5 × 10^{9}×365×24×60×60 secNumber of atoms, N = 6.023×10^{23}/238

Activity , A = λN

$\displaystyle A = \frac{0.693}{T_{1/2}} \times N $

$\displaystyle A = \frac{0.693}{4.5 \times 10^9 \times 365 \times 24 \times 60 \times 60} \times 6.023 \times 10^{23}/238$

= 1.23 ×10^{4 } dps