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A nucleus of mass number 189 splits into two nuclei having mass number 125 and 64. The ratio of radius of two daughter nuclei respectively is:
- a)4 : 5
- b)5 : 4
- c)25 : 16
- d)1 : 1
Correct answer is option 'B'. Can you explain this answer?
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A nucleus of mass number 189 splits into two nuclei having mass number...
Nuclear Radius:
R = R0(A)1/3
R = R0(A)1/3
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A nucleus of mass number 189 splits into two nuclei having mass number...
Given:
- Mass number of parent nucleus = 189
- Mass numbers of two daughter nuclei = 125 and 64
To find:
The ratio of the radii of the two daughter nuclei.
Solution:
The mass number of a nucleus represents the sum of protons and neutrons in the nucleus. Since the mass number of the parent nucleus is 189, it can be written as the sum of the mass numbers of the two daughter nuclei:
189 = 125 + 64
Now, let's assume the radii of the two daughter nuclei as r1 and r2 respectively.
The ratio of the radii is given as:
r1/r2 = √(A1/A2)
where A1 and A2 are the mass numbers of the daughter nuclei.
Substituting the given values:
r1/r2 = √(125/64)
Simplifying further:
r1/r2 = √(5/4)
To rationalize the denominator, we multiply both the numerator and denominator by √4:
r1/r2 = (√5/√4) * (√4/√4)
r1/r2 = (√5/2) * (1/2)
r1/r2 = √5/4
Therefore, the ratio of the radii of the two daughter nuclei is 5:4.
Hence, the correct answer is option B) 5:4.
- Mass number of parent nucleus = 189
- Mass numbers of two daughter nuclei = 125 and 64
To find:
The ratio of the radii of the two daughter nuclei.
Solution:
The mass number of a nucleus represents the sum of protons and neutrons in the nucleus. Since the mass number of the parent nucleus is 189, it can be written as the sum of the mass numbers of the two daughter nuclei:
189 = 125 + 64
Now, let's assume the radii of the two daughter nuclei as r1 and r2 respectively.
The ratio of the radii is given as:
r1/r2 = √(A1/A2)
where A1 and A2 are the mass numbers of the daughter nuclei.
Substituting the given values:
r1/r2 = √(125/64)
Simplifying further:
r1/r2 = √(5/4)
To rationalize the denominator, we multiply both the numerator and denominator by √4:
r1/r2 = (√5/√4) * (√4/√4)
r1/r2 = (√5/2) * (1/2)
r1/r2 = √5/4
Therefore, the ratio of the radii of the two daughter nuclei is 5:4.
Hence, the correct answer is option B) 5:4.
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A nucleus of mass number 189 splits into two nuclei having mass number 125 and 64. The ratio of radius of two daughter nuclei respectively is:a)4 : 5b)5 : 4c)25 : 16d)1 : 1Correct answer is option 'B'. Can you explain this answer?
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