Some amount of a radioactive substance (half-life =10 days ) is spread inside a room and consequently, the level of radiation becomes 50 times the…

Question

Some amount of a radioactive substance (half-life =10 days ) is spread inside a room and consequently, the level of radiation becomes 50 times the permissible level for normal occupancy of the room. After how many days will the room be safe for occupation?

MARKS Content Team · Accepted Answer

Correct answer: (C) 56.4 days. since, the initial activity is 50 times the activity for safe occupancy, therefore R_0=50R, where R=λN. since, R∝N (RR_0=NN_0=12^n=12^(t/T)Or 12^(t/10)=1502^(t/10)-50⇒t)/10log_102=log_1050 ⇒ t=10log_1050/log102=(10×1.699)/0.301=56.4 days

Some amount of a radioactive substance (half-life $= 10$ days ) is spread inside a room and consequently, the level of radiation becomes $50$ times the permissible level for normal occupancy of the room. After how many days will the room be safe for occupation?

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