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The counting rate observed from a radioactive source at t = 0 second was 1600 counts per second and t = 8 seconds it was 100 counts per second. The counting rate observed as counts per second t = 6 seconds will be

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400

200

250

300

answer is D.

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Detailed Solution

t no. counts/sec
0 1600
2 800
4 400
6 200
8 100

$∴$ at t = 6s is 200 cps

$\frac{dN}{dt} = - λN$

$\frac{{λN}_{0}}{λN} = \frac{1600}{100}$

$\frac{N_{0}}{N} = 16; or N = \frac{N_{0}}{16} = \frac{N_{0}}{2^{4}}$

$4 half life time = 8 s e c$

$T_{\frac{1}{2}} = 2 s e c; 6 s e c = 3 T_{\frac{1}{2}}$

$\frac{dN}{dt} = \frac{1600}{2^{3}} = 200$

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