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Two elements A and B with atomic numbers ZA and ZB are used to produce characteristic x–rays with frequencies A and B respectively. If ZA : ZB= 1 : 2, then vA : vB will be
- a)1 :√2
- b)1 : 8
- c)4 : 1
- d)1 : 4
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Two elements A and B with atomic numbers ZA and ZB are used to produce...
√v = a(z - b) , Ignoring screening effect (i.e. b=0)
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Two elements A and B with atomic numbers ZA and ZB are used to produce...
Understanding Characteristic X-Rays
Characteristic x-rays are emitted when electrons transition between energy levels in an atom. The frequency of emitted x-rays is directly related to the atomic number of the element.
Relation Between Atomic Number and Frequency
The frequency of the characteristic x-rays produced by an element is proportional to the square of its atomic number (Z). This relationship can be expressed as follows:
- v ∝ Z²
Given Condition
In this problem, we have two elements A and B with atomic numbers:
- ZA : ZB = 1 : 2
This means:
- ZA = k (for some constant k)
- ZB = 2k
Calculating Frequencies
Using the relationship v ∝ Z², we can express the frequencies:
- vA ∝ (ZA)² = (k)² = k²
- vB ∝ (ZB)² = (2k)² = 4k²
Now, we can find the ratio of frequencies vA to vB:
- vA : vB = k² : 4k²
This simplifies to:
- vA : vB = 1 : 4
Conclusion
Thus, the correct answer for the ratio of frequencies vA : vB is:
- 1 : 4 (Option D)
This demonstrates that as the atomic number increases, the frequency of the emitted x-rays increases significantly due to the square relationship.
Characteristic x-rays are emitted when electrons transition between energy levels in an atom. The frequency of emitted x-rays is directly related to the atomic number of the element.
Relation Between Atomic Number and Frequency
The frequency of the characteristic x-rays produced by an element is proportional to the square of its atomic number (Z). This relationship can be expressed as follows:
- v ∝ Z²
Given Condition
In this problem, we have two elements A and B with atomic numbers:
- ZA : ZB = 1 : 2
This means:
- ZA = k (for some constant k)
- ZB = 2k
Calculating Frequencies
Using the relationship v ∝ Z², we can express the frequencies:
- vA ∝ (ZA)² = (k)² = k²
- vB ∝ (ZB)² = (2k)² = 4k²
Now, we can find the ratio of frequencies vA to vB:
- vA : vB = k² : 4k²
This simplifies to:
- vA : vB = 1 : 4
Conclusion
Thus, the correct answer for the ratio of frequencies vA : vB is:
- 1 : 4 (Option D)
This demonstrates that as the atomic number increases, the frequency of the emitted x-rays increases significantly due to the square relationship.
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Two elements A and B with atomic numbers ZA and ZB are used to produce characteristic x–rays with frequencies A and B respectively. If ZA : ZB= 1 : 2, then vA: vBwill bea)1 :√2b)1 : 8c)4 : 1d)1 : 4Correct answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two elements A and B with atomic numbers ZA and ZB are used to produce characteristic x–rays with frequencies A and B respectively. If ZA : ZB= 1 : 2, then vA: vBwill bea)1 :√2b)1 : 8c)4 : 1d)1 : 4Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two elements A and B with atomic numbers ZA and ZB are used to produce characteristic x–rays with frequencies A and B respectively. If ZA : ZB= 1 : 2, then vA: vBwill bea)1 :√2b)1 : 8c)4 : 1d)1 : 4Correct answer is option 'D'. Can you explain this answer?.
Two elements A and B with atomic numbers ZA and ZB are used to produce characteristic x–rays with frequencies A and B respectively. If ZA : ZB= 1 : 2, then vA: vBwill bea)1 :√2b)1 : 8c)4 : 1d)1 : 4Correct answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two elements A and B with atomic numbers ZA and ZB are used to produce characteristic x–rays with frequencies A and B respectively. If ZA : ZB= 1 : 2, then vA: vBwill bea)1 :√2b)1 : 8c)4 : 1d)1 : 4Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two elements A and B with atomic numbers ZA and ZB are used to produce characteristic x–rays with frequencies A and B respectively. If ZA : ZB= 1 : 2, then vA: vBwill bea)1 :√2b)1 : 8c)4 : 1d)1 : 4Correct answer is option 'D'. Can you explain this answer?.
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