Question

The activity of a radioactive substance is 4700 per minute. Five minute later the activity is 2700 per minute. Find a) decay constant and b) haltf-life of the radioactive substance.

Answer 1

a) Decay constant is $<strong>0.1109min^{-1}$

b) Halt-life of the radioactive substance is $6.2min$

Explanation:

a) Expression for rate law for first order kinetics is given by:

$A=A_0e^{-kt}$

where,

k = rate constant  

t = time for decomposition = 5 minutes

A = activity at time t = 2700

$A_0$ = initial activity  = 4700  

$2700=4700\times e^{-k\times 5}$

$k=0.1109min^{-1}$

b) half-life of the radioactive substance:

Half life is the amount of time taken by a radioactive material to decay to half of its original value.

$t_{\frac{1}{2}}=\frac{0.69}{k}$

$t_{\frac{1}{2}}=\frac{0.69}{0.1109}=6.2min$

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