Physics-
General
Easy

Question

A radioactive sample at any instant has its disintegration rate 5000 disintegrations per minute. After 5 min, the rate is 1250 disintegrations per min. Then, the decay constant (per minute) is

  1. 0.4 In 2
  2. 0.2 In 2
  3. 0.1 In 2
  4. 0.8 In 2

The correct answer is: 0.4 In 2


    Given N subscript 0 lambda equals 5000 comma N lambda equals 1250
    N equals N subscript 0 e to the power of negative lambda t end exponent equals N subscript 0 e to the power of negative 5 lambda end exponent
    Where lambda is decay constant per min
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell N lambda equals N subscript 0 lambda e to the power of negative 5 lambda end exponent end cell row cell 1250 equals N subscript 0 lambda e to the power of negative 5 lambda end exponent end cell row cell therefore e to the power of negative 5 lambda end exponent equals 5000 over 1250 equals 4 end cell row cell e to the power of 5 lambda end exponent equals 4 end cell row cell 5 lambda equals 2 log subscript e invisible function application 2 end cell row cell lambda equals 0.4 ln invisible function application 2 end cell end table






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