Question

1gram of a radioactive substance takes 50 seconds to loose 1 centigram. find its half life

Answer 1

N=N°e^-Xt
N= substance left (here is 0.99 gram)
N° = Initial amount (1 gram)
t = 50s
Find X
Half life is ln 2/X

Answer 2

Half life of radioactive substance is 7.7 seconds

Explanation:

Radioactive decay follows first order kinetics.

$N=N_o\times e^{-\lambda t}$

N = amount left after time t  = 1 cg =  0.01 g

$N_0$ = initial amount  = 1 g

$\lambda$ = rate constant  = ?

t= time  = 50 sec

$0.01g=1g\times e^{-\lambda\times 50s}$

$\lambda=0.09s^{-1}}$

Relation of rate constant and half life

$\lambda =\frac{0.693}{t_{\frac{1}{2}}}$

$0.09=\frac{0.693}{t_{\frac{1}{2}}}$

$t_{\frac{1}{2}}=7.7s$

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