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Consider a particle of mass m bound a square well of length L and depth of potential V, the mini- mum kinetic energy required to pass the potential
barier is
(a) hbar^ 2 m L ^ 2
(b) hbar^ 2 m * L ^ 2
c) hbar^ 2 8m * L ^ 2 (
(d) h^ / m 8L ^ 2?
barier is
(a) hbar^ 2 m L ^ 2
(b) hbar^ 2 m * L ^ 2
c) hbar^ 2 8m * L ^ 2 (
(d) h^ / m 8L ^ 2?
Most Upvoted Answer
Consider a particle of mass m bound a square well of length L and dept...
Understanding the Potential Barrier in Quantum Mechanics
In quantum mechanics, a particle confined in a potential well can encounter a barrier. The minimum kinetic energy required to surmount this barrier is crucial for understanding tunneling phenomena.
Potential Well Characteristics
- Length of the well: L
- Depth of the potential: V
- Mass of the particle: m
Minimum Kinetic Energy
To escape the potential barrier, the particle must possess sufficient kinetic energy. The minimum kinetic energy (K.E.) to overcome a potential barrier is derived from the principles of quantum mechanics and energy conservation.
Key Considerations
- The kinetic energy must equal the potential energy at the barrier for the particle to escape.
- The energy levels in the well are quantized, and the kinetic energy is related to the wavefunction of the particle.
Correct Answer Derivation
The minimum kinetic energy required to pass the potential barrier can be expressed as:
- The kinetic energy K.E. is proportional to the reduced Planck constant (hbar), mass (m), and the square of the well length (L).
From the options given, the expression that matches this relationship is:
- (c) hbar^2 / (8m * L^2)
This expression indicates that as the mass increases or the well length increases, the required kinetic energy decreases.
Conclusion
Understanding the kinetic energy required helps in analyzing quantum tunneling, which is pivotal in various physical phenomena including nuclear fusion and semiconductor physics. The minimum kinetic energy to overcome a potential barrier in this context is best represented by option (c).
In quantum mechanics, a particle confined in a potential well can encounter a barrier. The minimum kinetic energy required to surmount this barrier is crucial for understanding tunneling phenomena.
Potential Well Characteristics
- Length of the well: L
- Depth of the potential: V
- Mass of the particle: m
Minimum Kinetic Energy
To escape the potential barrier, the particle must possess sufficient kinetic energy. The minimum kinetic energy (K.E.) to overcome a potential barrier is derived from the principles of quantum mechanics and energy conservation.
Key Considerations
- The kinetic energy must equal the potential energy at the barrier for the particle to escape.
- The energy levels in the well are quantized, and the kinetic energy is related to the wavefunction of the particle.
Correct Answer Derivation
The minimum kinetic energy required to pass the potential barrier can be expressed as:
- The kinetic energy K.E. is proportional to the reduced Planck constant (hbar), mass (m), and the square of the well length (L).
From the options given, the expression that matches this relationship is:
- (c) hbar^2 / (8m * L^2)
This expression indicates that as the mass increases or the well length increases, the required kinetic energy decreases.
Conclusion
Understanding the kinetic energy required helps in analyzing quantum tunneling, which is pivotal in various physical phenomena including nuclear fusion and semiconductor physics. The minimum kinetic energy to overcome a potential barrier in this context is best represented by option (c).
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Consider a particle of mass m bound a square well of length L and depth of potential V, the mini- mum kinetic energy required to pass the potentialbarier is(a) hbar^ 2 m L ^ 2(b) hbar^ 2 m * L ^ 2c) hbar^ 2 8m * L ^ 2 ((d) h^ / m 8L ^ 2?
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Consider a particle of mass m bound a square well of length L and depth of potential V, the mini- mum kinetic energy required to pass the potentialbarier is(a) hbar^ 2 m L ^ 2(b) hbar^ 2 m * L ^ 2c) hbar^ 2 8m * L ^ 2 ((d) h^ / m 8L ^ 2? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Consider a particle of mass m bound a square well of length L and depth of potential V, the mini- mum kinetic energy required to pass the potentialbarier is(a) hbar^ 2 m L ^ 2(b) hbar^ 2 m * L ^ 2c) hbar^ 2 8m * L ^ 2 ((d) h^ / m 8L ^ 2? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a particle of mass m bound a square well of length L and depth of potential V, the mini- mum kinetic energy required to pass the potentialbarier is(a) hbar^ 2 m L ^ 2(b) hbar^ 2 m * L ^ 2c) hbar^ 2 8m * L ^ 2 ((d) h^ / m 8L ^ 2?.
Consider a particle of mass m bound a square well of length L and depth of potential V, the mini- mum kinetic energy required to pass the potentialbarier is(a) hbar^ 2 m L ^ 2(b) hbar^ 2 m * L ^ 2c) hbar^ 2 8m * L ^ 2 ((d) h^ / m 8L ^ 2? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Consider a particle of mass m bound a square well of length L and depth of potential V, the mini- mum kinetic energy required to pass the potentialbarier is(a) hbar^ 2 m L ^ 2(b) hbar^ 2 m * L ^ 2c) hbar^ 2 8m * L ^ 2 ((d) h^ / m 8L ^ 2? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a particle of mass m bound a square well of length L and depth of potential V, the mini- mum kinetic energy required to pass the potentialbarier is(a) hbar^ 2 m L ^ 2(b) hbar^ 2 m * L ^ 2c) hbar^ 2 8m * L ^ 2 ((d) h^ / m 8L ^ 2?.
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Consider a particle of mass m bound a square well of length L and depth of potential V, the mini- mum kinetic energy required to pass the potentialbarier is(a) hbar^ 2 m L ^ 2(b) hbar^ 2 m * L ^ 2c) hbar^ 2 8m * L ^ 2 ((d) h^ / m 8L ^ 2?, a detailed solution for Consider a particle of mass m bound a square well of length L and depth of potential V, the mini- mum kinetic energy required to pass the potentialbarier is(a) hbar^ 2 m L ^ 2(b) hbar^ 2 m * L ^ 2c) hbar^ 2 8m * L ^ 2 ((d) h^ / m 8L ^ 2? has been provided alongside types of Consider a particle of mass m bound a square well of length L and depth of potential V, the mini- mum kinetic energy required to pass the potentialbarier is(a) hbar^ 2 m L ^ 2(b) hbar^ 2 m * L ^ 2c) hbar^ 2 8m * L ^ 2 ((d) h^ / m 8L ^ 2? theory, EduRev gives you an
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