Question

A nuclear power plant operates at 40.0% efficiency with a continuous production of 1002 MW of usable power in 1.00 year and consumes 1.03×10⁶ g of uranium-235 in this time period. What is the energy in joules released by the fission of a single uranium-235 atom?

Answer 1

Given,

Mass of uranium-235 = 1.03 x 10⁶ g

Time(T) = 1.00 year

Usable power production = 1002 MW

We Know,

1 Watt = 1 J /s

Now, the power plant operates at 40.0 % efficiency, Thus the original amount of power production from U-235 is,

40 % = ( 1002 MW / Original amount of power production) x 100

Thus,

The original amount of power production = 2505 MW

Converting MW to J/s,

= 2505 MW x ( 10⁶ watt / 1 MW) x (1 J/s / 1 Watt) = 2.505x 10⁹ J/s

Now,

Calculating the original energy production in 1 year,

= 1 year x (365 days/1 year) x (24 Hours /1 day) x (60 minutes/ 1 hour) x (60 seconds / 1minute) x ( 2.505x 10⁹ J / 1 sec)

= 7.8998 x 10¹⁶ J

Now, Calculating the number of atoms of U-235 from the given mass,

= 1.03 x 10⁶ g U-235 x ( 1 mol /235 g) x ( 6.023x10²³/1 mol)

= 2.6398 x10²⁷ atoms of U-235

Now, Evergy in joules released by the fission of a single uranium-235 atom is,

= 7.8998 x 10¹⁶ J / 2.6398 x10²⁷ atoms of U-235

= 2.99 x 10^-11 J / atom of U-235