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Two particles are said to be distinguishable when
- a)Their total wave-function is anti-symmetric under exchange of particles.
- b)Their wave-functions are overlapping in space
- c)The mean free path of the particles is large compared to their de-Broglie wavelength.
- d)The permutation of particles within a given configuration does not lead to a new state.
Correct answer is option 'C'. Can you explain this answer?
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Two particles are said to be distinguishable whena)Their total wave-fu...
In Quantum mechanical description of particles, the de-Broglie wavelength of a particles is a measure of the wave character of the particle and hence, in a way, measures the inherent imprecision in locating a particle. It means that a particle is speed over a length and not localized at precisely fixed spot. Hence, the average distance between two particles (mean free path) should be large as compared to their de-Broglie wavelength for them to be ‘distinguishable’.
Options (a) and (d) are properties that are associated with ‘indistingunishable’ particles.
Options (a) and (d) are properties that are associated with ‘indistingunishable’ particles.
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Two particles are said to be distinguishable whena)Their total wave-fu...
Distinguishable particles and their properties
Distinguishable particles are those that can be easily differentiated from each other based on their properties such as mass, charge, spin, etc. The following points explain the distinguishing features of distinguishable particles:
- Total wave-function: In quantum mechanics, the total wave-function of a system of particles is given by the product of individual wave-functions of each particle. For distinguishable particles, the total wave-function is symmetric under exchange of particles. This means that the wave-function remains unchanged when the particles are interchanged.
- Overlapping wave-functions: When the wave-functions of two particles overlap in space, it means that there is a possibility of the particles interacting with each other through various physical processes such as scattering, collision, etc. This is a characteristic feature of distinguishable particles.
- Mean free path: Mean free path is defined as the average distance traveled by a particle between successive collisions with other particles. For distinguishable particles, the mean free path is large compared to their de-Broglie wavelength. This is because distinguishable particles do not interact frequently with each other, and hence, they can travel longer distances without any significant change in their motion.
- Permutation of particles: Permutation refers to the interchanging of particles within a given configuration. For distinguishable particles, the permutation of particles within a given configuration does not lead to a new state. This is because the properties of each particle remain unchanged even after the permutation.
Conclusion
Out of the given options, option 'C' is the correct answer because it defines the distinguishing feature of distinguishable particles based on their mean free path and de-Broglie wavelength. The mean free path of distinguishable particles is large compared to their de-Broglie wavelength, which means that these particles do not interact frequently with each other, and hence, they can travel longer distances without any significant change in their motion.
Distinguishable particles are those that can be easily differentiated from each other based on their properties such as mass, charge, spin, etc. The following points explain the distinguishing features of distinguishable particles:
- Total wave-function: In quantum mechanics, the total wave-function of a system of particles is given by the product of individual wave-functions of each particle. For distinguishable particles, the total wave-function is symmetric under exchange of particles. This means that the wave-function remains unchanged when the particles are interchanged.
- Overlapping wave-functions: When the wave-functions of two particles overlap in space, it means that there is a possibility of the particles interacting with each other through various physical processes such as scattering, collision, etc. This is a characteristic feature of distinguishable particles.
- Mean free path: Mean free path is defined as the average distance traveled by a particle between successive collisions with other particles. For distinguishable particles, the mean free path is large compared to their de-Broglie wavelength. This is because distinguishable particles do not interact frequently with each other, and hence, they can travel longer distances without any significant change in their motion.
- Permutation of particles: Permutation refers to the interchanging of particles within a given configuration. For distinguishable particles, the permutation of particles within a given configuration does not lead to a new state. This is because the properties of each particle remain unchanged even after the permutation.
Conclusion
Out of the given options, option 'C' is the correct answer because it defines the distinguishing feature of distinguishable particles based on their mean free path and de-Broglie wavelength. The mean free path of distinguishable particles is large compared to their de-Broglie wavelength, which means that these particles do not interact frequently with each other, and hence, they can travel longer distances without any significant change in their motion.
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Two particles are said to be distinguishable whena)Their total wave-function is anti-symmetric under exchange of particles.b)Their wave-functions are overlapping in spacec)The mean free path of the particles is large compared to their de-Broglie wavelength.d)The permutation of particles within a given configuration does not lead to a new state.Correct answer is option 'C'. Can you explain this answer?
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Two particles are said to be distinguishable whena)Their total wave-function is anti-symmetric under exchange of particles.b)Their wave-functions are overlapping in spacec)The mean free path of the particles is large compared to their de-Broglie wavelength.d)The permutation of particles within a given configuration does not lead to a new state.Correct answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Two particles are said to be distinguishable whena)Their total wave-function is anti-symmetric under exchange of particles.b)Their wave-functions are overlapping in spacec)The mean free path of the particles is large compared to their de-Broglie wavelength.d)The permutation of particles within a given configuration does not lead to a new state.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two particles are said to be distinguishable whena)Their total wave-function is anti-symmetric under exchange of particles.b)Their wave-functions are overlapping in spacec)The mean free path of the particles is large compared to their de-Broglie wavelength.d)The permutation of particles within a given configuration does not lead to a new state.Correct answer is option 'C'. Can you explain this answer?.
Two particles are said to be distinguishable whena)Their total wave-function is anti-symmetric under exchange of particles.b)Their wave-functions are overlapping in spacec)The mean free path of the particles is large compared to their de-Broglie wavelength.d)The permutation of particles within a given configuration does not lead to a new state.Correct answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Two particles are said to be distinguishable whena)Their total wave-function is anti-symmetric under exchange of particles.b)Their wave-functions are overlapping in spacec)The mean free path of the particles is large compared to their de-Broglie wavelength.d)The permutation of particles within a given configuration does not lead to a new state.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two particles are said to be distinguishable whena)Their total wave-function is anti-symmetric under exchange of particles.b)Their wave-functions are overlapping in spacec)The mean free path of the particles is large compared to their de-Broglie wavelength.d)The permutation of particles within a given configuration does not lead to a new state.Correct answer is option 'C'. Can you explain this answer?.
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Two particles are said to be distinguishable whena)Their total wave-function is anti-symmetric under exchange of particles.b)Their wave-functions are overlapping in spacec)The mean free path of the particles is large compared to their de-Broglie wavelength.d)The permutation of particles within a given configuration does not lead to a new state.Correct answer is option 'C'. Can you explain this answer?, a detailed solution for Two particles are said to be distinguishable whena)Their total wave-function is anti-symmetric under exchange of particles.b)Their wave-functions are overlapping in spacec)The mean free path of the particles is large compared to their de-Broglie wavelength.d)The permutation of particles within a given configuration does not lead to a new state.Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of Two particles are said to be distinguishable whena)Their total wave-function is anti-symmetric under exchange of particles.b)Their wave-functions are overlapping in spacec)The mean free path of the particles is large compared to their de-Broglie wavelength.d)The permutation of particles within a given configuration does not lead to a new state.Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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