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A radio nuclide with disintegration cons...

A radio nuclide with disintegration constant `lambda` is produced in a reactor at a constant rate `alpha` nuclei per second. During each decay energy `E_0` is released. `20%` of this energy is utilized in increasing the temperature of water. Find the increase in temperature of `m` mass of water in time `t`. Specific heat of water is `s`. Assume that there is no loss of energy through water surface.

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The correct Answer is:
`DeltaT = (0.2E_(0)[alphat-(alpha)/(lambda)(1-e^(-lambdat))])/(mS)`
Production of radioactive nudel `=alpha//sec`
Disintegration `=lambdaN_(A)`
At any time `t=(dN_(A))/(dt)=alpha-lambdaN_(A)`
`implies underset(0)overset(N_(A))(int) (dN_(A))/(alpha-lambdaN_(A))=underset(0)overset(t)(int) dt implies N_(A)=alpha/lambda (1-e^(-lambdat))`
Nuclei disinterated `=alphat-N_(A)=alpha[t-1/lambda(1-e^(-lambdat))]`
Total energy produced `=E_(0)[alphat-alpha/lambda (1-e^(-lambdat))]`
Energy used in water heating
`=0.2E_(0)[alphat-alpha/lambda(1-e^(-lambdat))]=msDeltaT`
`DeltaT=(0.2 E_(0)[alphat-alpha//lambda(1-e^(-lambdat))])/(mS)`
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ALLEN -SIMPLE HARMONIC MOTION-Exercise-04 [B]
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  3. A radio nuclide with disintegration constant lambda is produced in a r...

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  4. If 13.6 eV energy is required to ionized the hydrogen atom then , the...

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  5. If the binding energy of the electron in a hydrogen atom is 13.6 eV, t...

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  6. Which of the following atoms has the lowest ionization potential ?

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  7. The wavelength involved in the spectrum of deuterium (.(1)^(2)D) are s...

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  8. The manifestation of band structure in solids is due to

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  9. The diagram shows the energy levels for an electron in a certain atom....

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  10. Which of the following transitions in hydrogen atoms emit photons of h...

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  11. Suppose an electron is attracted towards the origin by a force (k)/(r ...

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  12. The transtion from the state n = 4 to n = 3 in a hydrogen like atom r...

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  13. Energy required for the electron excitation in Li^(+2) from the first ...

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  14. Hydrogen atom is excited from ground state to another state with princ...

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  15. Dia-atomic molecule is composed of masses m(1) and m(2) and distance b...

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  16. In a hydrogen like atom electron make transition from an energy level ...

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  17. Hydrogen (""(1)H^(1)), Deuterium (""(1)H^(2)), single ionised Helium (...

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  18. The radiation corresponding to 3 to 2 transition of hydrogen atom fall...

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  19. Work function of sodium and copper is 2.3 eV and 4.5 eV respectively.R...

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  20. Formation of covalent bonds in compounds exhibits …….nature.

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