Chapter 11: Q65E (page 520)

(a) To release 100 MW of power, approximately how many uranium fissions must occur every second?
(b) How many kilograms of U-235 would have to fission in 1 year?

Short Answer

Expert verified

(a) $N_{Y} = 9.859 \times 10^{25} decays/year$

(b) $M = 38.5 k g$

Step by step solution

Given data

Given that the power released by the fission reaction is :

$P = 100 M W = 100 \times 10^{6} W$

Then energy is:

$Q = 200 M e V = 200 \times 1.6 \times 10^{- 13} J = 320 \times 10^{- 13} J$

Find the Number of uranium-235 fissions that will occur

(a)

The Number of fission required for the release of 100 MW of energy is:

$N = \frac{P}{Q} = \frac{10^{8} W}{320 \times 10^{- 13} J} = 3.12 \times 10^{18} decays/second$

Let's calculate the Number of fission that would happen in a year,

$N_{y} = N \times 3.16 \times 10^{7} = 9.859 \times 10^{25} decays/year$

Therefore, the Number of fission will be $N_{Y} {= 9.859×10}^{25} decays/year$ .

Finding the Mass of uranium-235.

Mass of uranium-235 that would be decayed to release the power of 100 MeV for a year is:

$\begin{array}{rcl} M & = & N_{Y} \times m_{U r_{235}} \\ = & 9.89 \times 10^{25} \times 235 u \times 1.66 \times 10^{- 27} k g / u \\ = & 38.5 k g \end{array}$

Thus, the Mass of the uranium is $38.5 k g$ .

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(a) To release 100 MW of power, approximately how many uranium fissions must occur every second?
(b) How many kilograms of U-235 would have to fission in 1 year?

Short Answer

Step by step solution

Given data

Find the Number of uranium-235 fissions that will occur

Finding the Mass of uranium-235.

One App. One Place for Learning.

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Study anywhere. Anytime. Across all devices.

(a) To release 100 MW of power, approximately how many uranium fissions must occur every second?(b) How many kilograms of U-235 would have to fission in 1 year?

Short Answer

Step by step solution

Given data

Find the Number of uranium-235 fissions that will occur

Finding the Mass of uranium-235.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Wave Optics

Oscillations

Rotational Dynamics

Quantum Physics

Famous Physicists

Electromagnetism

Study anywhere. Anytime. Across all devices.

(a) To release 100 MW of power, approximately how many uranium fissions must occur every second?
(b) How many kilograms of U-235 would have to fission in 1 year?