The energy released by the fission of a single uranium nucleus is 200 MeV. The number of fissions of uranium nucleus per second required to produce 16 MW of power is

To determine the number of fissions of a uranium nucleus required to produce 16 MW of power, we first need to convert the power output into a compatible unit with the energy released per fission. The energy released by the fission of a single uranium nucleus is given as 200 MeV (mega-electronvolts). Let's break this down step by step.

Understanding the Units

Power is defined as the rate at which energy is produced or consumed. In this case, we have:

• Power (P) = 16 MW = 16 x 10^6 watts
• Energy per fission (E) = 200 MeV

Converting Energy from MeV to Joules

Next, we need to convert the energy released per fission from MeV to joules, since 1 joule is equivalent to 6.242 x 10^12 MeV. Therefore:

E (in joules) = 200 MeV × (1.602 x 10^-13 joules/MeV)

Calculating this gives:

E = 200 × 1.602 x 10^-13 = 3.204 x 10^-11 joules

Calculating the Number of Fissions

Now that we have the energy per fission in joules, we can find out how many fissions are needed to produce 16 MW of power. The formula to find the number of fissions per second (N) is:

N = Power / Energy per fission

Substituting the values we have:

N = (16 x 10^6 watts) / (3.204 x 10^-11 joules)

Performing the Calculation

Now, let's calculate N:

N = 16 x 10^6 / 3.204 x 10^-11 ≈ 4.99 x 10^17 fissions per second

Final Result

Thus, to produce 16 MW of power, approximately 4.99 x 10^17 fissions of uranium nuclei are required each second. This illustrates the immense energy potential contained within nuclear fission and highlights why it is a powerful source of energy in nuclear reactors.