Question

In: Chemistry

What is the half-life (T1/2) of a radioactive element with the following conditions? -Initial Activity =...

What is the half-life (T1/2) of a radioactive element with the following conditions?

-Initial Activity = 1000 milliCuries

-Final Activity = 400 milliCuries

-Elapsed Time= 20.0 days

Expert Solution

All radio active elements undergo first order reactions

For a first order reaction rate constant , k = ( 2.303 /t )x log ( A_o / A)

Where

A_o = initial activity = 1000 mC

A = final activity = 400 mC

t = time = 20.0 days

= 20.0x24x60x60 s

= 1728000 s

Plug the values we get

k = ( 2.303 /t )x log ( A_o / A)

k = ( 2.303 /1728000 )x log ( 1000/400 )

= 5.30x10^-7 s^-1

Half-life of first order reaction , t_1/2 = 0.693/k

= 0.693 / (5.30x10^-7 )

= 1.307x10⁶ s

= 1.307x10⁶ /(60x60x24) days

= 15.1 days

Therefore the half life is 15.1 days

queen_honey_blossom answered 4 months ago

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