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The radionuclide .^(56)Mn is being produ...

The radionuclide `.^(56)Mn` is being produced in a cyclontron at a constant rate `P` by bombarding a manganese target with deutrons. `.^(56)Mn` has a half-life of `2.5 h` and the target contains large numbers of only the stable manganese isotopes `.^(56)Mn`. The reaction that produces `^(56)Mn` is
`.^(56)Mn` +`d` rarr `.^(56)Mn` +`p`
After being bombarded for a long time, the activity of `.^(56)Mn` becomes constant, equal to `13.86 xx 10^(10) s^(-1)`. (Use `l n2=0.693`, Avagadro number` =6 xx 10^(23)`, atomic weight of `.^(56)Mn`=`56 g mol^(-1))`.
After the activity of `.^(56)Mn` becomes constant, number of `.^(56)Mn` nuclei present in the target is equal to .

A

`5xx10^(11)`

B

`20xx10^(11)`

C

`1.2xx10^(14)`

D

`1.8xx10^(15)`

Text Solution

Verified by Experts

The correct Answer is:
D
As Rate of decay `=` Rate of production
`rArr P =lambdaN " " rArrN=(P)/(lambda)`
`=(Pt_(1//2))/(l n_(2))" " =1.8xx10^(15)`
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The radionuclide .^(56)Mn is being produced in a cyclontron at a constant rate P by bombarding a manganese target with deutrons. .^(56)Mn has a half-life of 2.5 h and the target contains large numbers of only the stable manganese isotopes .^(56)Mn . The reaction that produces ^(56)Mn is .^(56)Mn +d rarr .^(56)Mn +p After being bombarded for a long time, the activity of .^(56)Mn becomes constant, equal to 13.86 xx 10^(10) s^(-1) . (Use 1 n2=0.693 , Avagardo number =6 xx 10^(2), atomic weight of .^(56)Mn=56 g mol^(-1) ). After the activity of .^(56)Mn becomes constant, number of .^(56)Mn nuclei present in the target is equal to .

The radionuclide .^(56)Mn is being produced in a cyclontron at a constant rate P by bombarding a manganese target with deutrons. .^(56)Mn has a half-life of 2.5 h and the target contains large numbers of only the stable manganese isotopes .^(56)Mn . The reaction that produces .^(56)Mn is .^(56)Mn +d rarr .^(56)Mn +p After being bombarded for a long time, the activity of .^(56)Mn becomes constant, equal to 13.86 xx 10^(10) s^(-1) . (Use 1 n2=0.693 , Avagardo number =6 xx 10^(2) , atomic weight of .^(56)Mn=56 g mol^(-1) ). After a long time bombardment, number .^(56)Mn nuclei present in the target depends upon.

The radionuclide .^(56)Mn is being produced in a cyclontron at a constant rate P by bombarding a manganese target with deutrons. .^(56)Mn has a half-life of 2.5 h and the target contains large numbers of only the stable manganese isotopes .^(56)Mn . The reaction that produces .^(56)Mn is .^(56)Mn +d rarr .^(56)Mn +p After being bombarded for a long time, the activity of .^(56)Mn becomes constant, equal to 13.86 xx 10^(10) s^(-1) . (Use 1 n2=0.693 , Avagardo number =6 xx 10^(2) , atomic weight of .^(56)Mn=56 g mol^(-1) ). At what constant rate P, .^(56)Mn nuclei are being produced in the cyclontron during the bombardment?

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