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A radioactive with decay constant lambda...

A radioactive with decay constant `lambda` is being produced in a nuclear ractor at a rate `q_(0)` per second, where `q_(0)` is a positive constant and t is the time. During each decay, `E_(0)` energy is released. The production of radionuclide starts at time `t=0`.
Instantaneous power developed at time t due to the decay of the radionuclide is .

A

(q_(0)t-q_(0)/(lambda)+q_(0)/(lambda)e^(-lambdat))E_(0)`

B

(q_(0)t+q_(0)/(lambda)-q_(0)/(lambda)e^(-lambdat))E_(0)`

C

(q_(0)t+q_(0)/(lambda)+q_(0)/(lambda)e^(-lambdat))E_(0)`

D

(q_(0)t+q_(0)/(lambda)-q_(0)/(lambda)e^(-lambdat))E_(0)`

Text Solution

Verified by Experts

The correct Answer is:
a
`N=(q_(0)t)/(lambda)-(q_(0))/(lambda^(2))+(q_(0))/(lambda^(2))e^(-lambdat)`
`P_(i nst)=lambdaNE_(0)=[q_(0)t-(q_(0))/(lambda)+(q_(0))/(lambda)e^(-lambdat)]E_(0)`.
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Knowledge Check

  • A radionuclide with decay constant lambda is being produced in a nuclear reactor at a rate a_(0) t per second, where a_(0) is positive constant and t is the time. During each decay, E_(0) energy is released. The production of radionuclide starts at time t=0 . Instantaneous power developed at time 't' due to the decay of the radionuclide is

    A
    `(a_(0)t+(a_(0))/(lambda)+(a_(0))/(lambda)e^(-lambda t))E_(0)`
    B
    `(a_(0)t+(a_(0))/(lambda)-(a_(0))/(lambda)e^(-lambda t))E_(0)`
    C
    `(a_(0)t-(a_(0))/(lambda)-(a_(0))/(lambda)e^(-lambda t))E_(0)`
    D
    `(A_(0)T-(a_(0))/(lambda)-(a_(0))/(lambda) e^(-lambdat)E_(0))`

  • A radioactive with decay constant lambda is being produced in a nuclear ractor at a rate q_0 per second, where q_(0) is a positive constant and t is the time. During each decay, E_(0) energy is released. The production of radionuclide starts at time t=0 . Average power developed in time t due to the decay of the radionuclide is

    A
    `((q_(0) t)/(2)-(q_(0))/(lambda) +(q_(0))/(lambda^(2)t) -(q_(0))/(lambda^(2)t) e^(-lambda t)E_(0))`
    B
    `((q_(0) t)/(2)+(q_(0))/(lambda) +(q_(0))/(lambda^(2)t) -(q_(0))/(lambda^(2)t) e^(-lambda t)E_(0))`
    C
    `((q_(0) t)/(2)-(q_(0))/(lambda) +(q_(0))/(lambda^(2)t) +(q_(0))/(lambda^(2)t) e^(-lambda t)E_(0))`
    D
    `((q_(0) t)/(2)+(q_(0))/(lambda) +(q_(0))/(lambda^(2)t) +(q_(0))/(lambda^(2)t) e^(-lambda t)E_(0))`

  • A radioactive with decay constant lambda is being produced in a nuclear ractor at a rate q_(0) per second, where q_(0) is a positive constant and t is the time. During each decay, E_(0) energy is released. The production of radionuclide starts at time t=0 . Which differential equation correctly represents the above process?.

    A
    `(dN)/(dt)+lambda N=q_(0) t`
    B
    `(dN)/(dt)-lambda N=q_(0) t`
    C
    `(dN)/(dt)+q_(0) t=lambda N`
    D
    `(dN)/(dt)+q_(0) t=-lambda N`

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