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A radioactive nuclide is produced at a c...

A radioactive nuclide is produced at a constant rate x nuclei per second. During each decay, `E_0` energy is released ,50% of this energy is utilised in melting ice at `0^@`C. Find mass of ice that will melt in one mean life. (`lambda`=decay consant, `L_f`=Latent heat of fusion )

Text Solution

Verified by Experts

The correct Answer is:
`(xE_(0))/(2lambdaeL_(f))`
`overset(x)(rarr)Aoverset(lambda)(rarr)B`
No. of neuleus disintegrated `=xt-x/lambda (1-e^(-lambdat))`
for `t=1/lambda`
Distegration `=x/lambda [1-1+e^(-1)]=x/(e lambda)`
Energy released `=(E_(0)x)/(e lambda)`
Energy utilized for melting `=0.5xx(E_(0)x)/(e lambda)`
Mass of ice melted `=(E_(0)x)/(2e lambdaL_(F))`
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