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A nucleus at rest splits into two nuclear parts having radii in the ratio 1 : 2. Their velocities are in the ratio
- a)8 : 1
- b)6 : 1
- c)4 : 1
- d)2 : 1
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A nucleus at rest splits into two nuclear parts having radii in the r...
Let A1 and A2 be the mass numbers of the two nuclear parts. Their radii are given by
R1 = R0 (A1)1/3 and R2 = R0 (A2)1/3
Dividing, we get
Hence the ratio of their masses is
m1 / m2 = 1/8
From the principle of conservation of momentum, the magnitude of p1 = magnitude of p2 or m1 v1 = m2 v2,
which gives
which is choice (a).
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Community Answer
A nucleus at rest splits into two nuclear parts having radii in the r...
Concept:
When a nucleus at rest undergoes fission, the conservation of linear momentum dictates that the total momentum before fission is equal to the total momentum after fission. This principle can be used to determine the relationship between the velocities of the two nuclear parts after fission.
Solution:
- Let the radii of the two nuclear parts be r and 2r, respectively.
- According to the question, the radii are in the ratio 1:2, i.e., r:2r = 1:2.
- The velocities of the nuclear parts will be inversely proportional to their radii. Therefore, the velocities will be in the ratio 2:1.
Therefore, the correct answer is:
a) 8:1
By understanding the concept of conservation of linear momentum and the relationship between the radii and velocities of the nuclear parts, we can easily determine the correct ratio of velocities in this scenario.
When a nucleus at rest undergoes fission, the conservation of linear momentum dictates that the total momentum before fission is equal to the total momentum after fission. This principle can be used to determine the relationship between the velocities of the two nuclear parts after fission.
Solution:
- Let the radii of the two nuclear parts be r and 2r, respectively.
- According to the question, the radii are in the ratio 1:2, i.e., r:2r = 1:2.
- The velocities of the nuclear parts will be inversely proportional to their radii. Therefore, the velocities will be in the ratio 2:1.
Therefore, the correct answer is:
a) 8:1
By understanding the concept of conservation of linear momentum and the relationship between the radii and velocities of the nuclear parts, we can easily determine the correct ratio of velocities in this scenario.
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A nucleus at rest splits into two nuclear parts having radii in the ratio 1 : 2. Their velocities are in the ratioa)8 : 1b)6 : 1c)4 : 1d)2 : 1Correct answer is option 'A'. Can you explain this answer?
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