Concept explainers
(a)
Prove that the number of fissions is given by the formula
(a)
Answer to Problem 60P
It is proved that the number of fissions is given by
Explanation of Solution
The number of fissions in 1st, 2nd, 3rd …. nth number is according to the series given below.
Write the equation to find the total number of fissions.
Conclusion:
Thus, it is proved that the number of fissions is given by
(b)
Time needed for the complete fission of uranium bomb.
(b)
Answer to Problem 60P
Time required will be
Explanation of Solution
Write the equation to find the number of uranium nuclei.
Here,
Write the equation to find the number of fissions given in part (a).
Write the equation to find the total time to complete fission from the time taken for the fission of one nucleus.
Here
Conclusion:
Substitute
Substitute
Substitute
So, the number of generations can be taken as 100.
Substitute 100 for
Thus, time required will be
(c)
Speed of sound in uranium.
(c)
Answer to Problem 60P
Speed is
Explanation of Solution
Write the equation to find the speed of sound through a medium.
Here,
Conclusion:
Substitute
Thus, the speed is
(d)
Time taken by compressional wave to cross the uranium sphere.
(d)
Answer to Problem 60P
Time taken is
Explanation of Solution
Write the equation for the volume of uranium sphere.
Here,
Express
Here,
Equate the right-hand sides of above two equations.
Write the equation to find the time taken by compressional wave to cross the uranium sphere.
Conclusion:
Substitute
Substitute
Thus, the time taken is
(d)
Check whether the bomb explained in part (b) can give energy by using all of its uranium and if possible, calculate the amount of energy in TNT.
(d)
Answer to Problem 60P
The entire uranium can undergo fission and it releases 107 kilotons of TNT.
Explanation of Solution
Time taken by the compressional wave to cross the entire uranium sphere is
Write the equation to find the energy released by the bomb.
Here,
Conclusion:
Substitute
Thus, the entire uranium can undergo fission and it releases 107 kilotons of TNT.
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Chapter 14 Solutions
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