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The two particle A and B have de Broglie wavelengths 1nm and 5nm re- spectively. If mass of A is 4 times that of mass of B, the ratio of KE of A and B would be 1) 5 : 1 2) 25 : 4 3) 20 : 1 4) 5 : 4?
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The two particle A and B have de Broglie wavelengths 1nm and 5nm re- s...
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The two particle A and B have de Broglie wavelengths 1nm and 5nm re- s...
Analysis of Kinetic Energy Ratio of Particles A and B
Explanation:
- Given data:
- λ(A) = 1nm
- λ(B) = 5nm
- Mass of A = 4 * Mass of B
- Relation between de Broglie wavelength and momentum:
- λ = h / p
- p = h / λ
- Relation between kinetic energy and momentum:
- KE = p^2 / 2m
- Calculating momentum for particles A and B:
- p(A) = h / λ(A) = h / 1nm
- p(B) = h / λ(B) = h / 5nm
- Calculating kinetic energy for particles A and B:
- KE(A) = p(A)^2 / 2m(A) = (h^2) / (2 * 1nm^2 * 4)
- KE(B) = p(B)^2 / 2m(B) = (h^2) / (2 * 5nm^2)
- Ratio of kinetic energies:
- KE(A) / KE(B) = [(h^2) / (2 * 1nm^2 * 4)] / [(h^2) / (2 * 5nm^2)]
- KE(A) / KE(B) = (1/4) / (1/10)
- KE(A) / KE(B) = 10 / 4
- KE(A) / KE(B) = 5 / 2
- Therefore, the ratio of the kinetic energies of particles A and B is 5 : 2.
Explanation:
- Given data:
- λ(A) = 1nm
- λ(B) = 5nm
- Mass of A = 4 * Mass of B
- Relation between de Broglie wavelength and momentum:
- λ = h / p
- p = h / λ
- Relation between kinetic energy and momentum:
- KE = p^2 / 2m
- Calculating momentum for particles A and B:
- p(A) = h / λ(A) = h / 1nm
- p(B) = h / λ(B) = h / 5nm
- Calculating kinetic energy for particles A and B:
- KE(A) = p(A)^2 / 2m(A) = (h^2) / (2 * 1nm^2 * 4)
- KE(B) = p(B)^2 / 2m(B) = (h^2) / (2 * 5nm^2)
- Ratio of kinetic energies:
- KE(A) / KE(B) = [(h^2) / (2 * 1nm^2 * 4)] / [(h^2) / (2 * 5nm^2)]
- KE(A) / KE(B) = (1/4) / (1/10)
- KE(A) / KE(B) = 10 / 4
- KE(A) / KE(B) = 5 / 2
- Therefore, the ratio of the kinetic energies of particles A and B is 5 : 2.
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The two particle A and B have de Broglie wavelengths 1nm and 5nm re- spectively. If mass of A is 4 times that of mass of B, the ratio of KE of A and B would be 1) 5 : 1 2) 25 : 4 3) 20 : 1 4) 5 : 4?
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The two particle A and B have de Broglie wavelengths 1nm and 5nm re- spectively. If mass of A is 4 times that of mass of B, the ratio of KE of A and B would be 1) 5 : 1 2) 25 : 4 3) 20 : 1 4) 5 : 4? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about The two particle A and B have de Broglie wavelengths 1nm and 5nm re- spectively. If mass of A is 4 times that of mass of B, the ratio of KE of A and B would be 1) 5 : 1 2) 25 : 4 3) 20 : 1 4) 5 : 4? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The two particle A and B have de Broglie wavelengths 1nm and 5nm re- spectively. If mass of A is 4 times that of mass of B, the ratio of KE of A and B would be 1) 5 : 1 2) 25 : 4 3) 20 : 1 4) 5 : 4?.
The two particle A and B have de Broglie wavelengths 1nm and 5nm re- spectively. If mass of A is 4 times that of mass of B, the ratio of KE of A and B would be 1) 5 : 1 2) 25 : 4 3) 20 : 1 4) 5 : 4? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about The two particle A and B have de Broglie wavelengths 1nm and 5nm re- spectively. If mass of A is 4 times that of mass of B, the ratio of KE of A and B would be 1) 5 : 1 2) 25 : 4 3) 20 : 1 4) 5 : 4? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The two particle A and B have de Broglie wavelengths 1nm and 5nm re- spectively. If mass of A is 4 times that of mass of B, the ratio of KE of A and B would be 1) 5 : 1 2) 25 : 4 3) 20 : 1 4) 5 : 4?.
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