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Chemical Kinetics

Question
CBSEENCH12010828

A radioactive element gets spilled over the floor of a room. Its half-life period is 30 days. If the initial activity is ten times the permissible value, after how many days will it be safe to enter the room ?

  • 1000 days

  • 300 days

  • 50 days

  • 100 days

Solution

D.

100 days

Activity space open parentheses negative dN over dt close parentheses space proportional to space straight N
straight N space equals space straight N subscript straight o open parentheses 1 half close parentheses to the power of straight n
straight N over straight N subscript straight o space equals space open parentheses 1 half close parentheses to the power of straight n
1 over 10 space equals open parentheses space 1 half close parentheses to the power of straight n
rightwards double arrow space 10 space equals space 2 to the power of straight n
log space 10 space equals space straight n space log 2
rightwards double arrow space straight n equals space fraction numerator 1 over denominator 0.301 end fraction space equals space 3.32
straight t space equals space straight n space straight x space straight t subscript 112
space equals space 3.32 space straight x space 30 space equals space 99.6 space days