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Question

# A radioactive material has a half life of 600 years and 300years for α and β emissions respectively. The material decays by simultaneous α and β emissions. What is time in which 34th of the material will decay?

A
600years
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B
900years
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C
220years
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D
400years
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Solution

## The correct option is C 220yearsA radioactive material has a half life=600 years for α emission.For β emission =300years respectivelyThe material decays by simultaneous α and β emissionsThe material decays time t when, the decay will be34th of the materialSolutionThe decay constant =λ is reciprocal of mean lifeλα=1600peryearand λβ=1300 per yearTotal decay constantλ=λα+λβ=1600+1300=1+2600=3600=1200 per yearWhen 34th per of sample has disintegrated.N=N04Let total sample =N01−34=N04thremainingN04=N0e−λte−λt=4λt=ln4t=1λln22t=2λln2=2×200ln2=277.25years

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