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 $38.5 k g$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

(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

Fields in Physics

Classical Mechanics

Work Energy and Power

Astrophysics

Oscillations

Space Physics

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

Fields in Physics

Classical Mechanics

Work Energy and Power

Astrophysics

Oscillations

Space Physics

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?