200 Mev energy is released when one nucleus of $^{235} U$ undergoes fission. Find the number of fissions per second required for producing a power of 1 mega watt

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$3.126 \times 10^{14}$

$3.125 \times 10^{13}$

$3.125 \times 10^{15}$

$3.125 \times 10^{16}$

answer is C.

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Detailed Solution

To calculate the number of fissions per second required to produce a power of 1 mega watt (MW) using the energy released per fission, we can follow these steps:

Convert the power from mega watts to watts.
1 MW = 1,000,000 watts

Convert the energy released per fission from MeV to joules.
$1 M e V = 1.6 x 10^{- 13} j o u l e s$ (approximately)

Calculate the number of fissions per second using the formula:
Power (in watts) = Number of fissions per second × Energy released per fission (in joules)

$1 M W = 1, 000, 000 w a t t s$

Energy released per fission $= 200 M e V = 200 x 1.6 x 10^{- 13} j o u l e s$

Energy released per fission $= 3.2 x 10^{- 11} j o u l e s$

Number of fissions per second = Power (in watts) / Energy released per fission (in joules)
Number of fissions per second $= \frac{1, 000, 000 w a t t s}{3.2 x 10^{- 11} j o u l e s}$