Calculating the Rate of Nuclear Fission with 1000 kW Power and 200 MeV Energy

[intellpuneet]

200 MeV of energy may be obtained per fission of U 235. A reactor is generating 1000 Kw of power. Find the rate of nuclear fission ?
Please help...

 

[da_nang]

You know the power, and you now the energy per fission. What are their definitions? How do you use them to get fission per second?

 

[WatermelonPig]

P = dW/dt = 1000000J/s

1 fission = 200 MeV = . . .

 

[da_nang]

You know that one fission gives 200 MeV energy. So the amount of energy per fission reaction is 200 MeV per fission reaction. If N is the number of fission reactions, this can be expressed as dE/dN. Now you want to find fission reaction per second, dN/dt.

How do you get dN/dt with dE/dN and dE/dt (power)?

 

[rwisz]

To calculate the rate of nuclear fission, we can use the formula:

Rate of fission = Power / Energy per fission

In this case, we have a power of 1000 kW and an energy per fission of 200 MeV. However, we need to convert the power from kilowatts to megaelectronvolts (MeV) in order to have consistent units.

1 kilowatt is equal to 6.241 x 10^15 MeV/s. Therefore, 1000 kW is equal to 6.241 x 10^18 MeV/s.

Now, we can plug these values into the formula:

Rate of fission = (6.241 x 10^18 MeV/s) / (200 MeV/fission)

= 3.1205 x 10^16 fissions/s

Therefore, the rate of nuclear fission in this scenario is approximately 3.1205 x 10^16 fissions per second. This high rate of fission is necessary to sustain the 1000 kW of power being generated by the reactor.