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Energy of Particle in Box along X axis Formula:
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The Energy of Particle in Box along X axis is defined as the quantized energy values that a particle can have when confined in a one-dimensional potential well. This is a fundamental concept in quantum mechanics that demonstrates the quantization of energy levels.
The calculator uses the particle in a box formula:
Where:
Explanation: The equation shows that energy is quantized and depends on the square of the quantum number, inversely proportional to both the mass of the particle and the square of the box length.
Details: This calculation is crucial for understanding quantum mechanical systems, semiconductor physics, and nanoscale devices where particle confinement leads to quantized energy states.
Tips: Enter the quantum number (positive integer), particle mass in kilograms, and box length in meters. All values must be positive and non-zero.
Q1: Why is energy quantized in a particle in a box?
A: Energy is quantized due to the boundary conditions imposed by the infinite potential well, which only allow specific wavefunctions (standing waves) to exist.
Q2: What are typical values for particle mass and box length?
A: For electrons, mass is approximately 9.11 × 10⁻³¹ kg. Box lengths in nanoscale systems range from 1-100 nm (1-100 × 10⁻⁹ m).
Q3: Can this formula be used for real-world applications?
A: Yes, it's used in quantum dots, nanowires, and other nanoscale devices where particle confinement occurs.
Q4: What happens when the quantum number increases?
A: Energy increases with the square of the quantum number, so higher energy levels are more widely spaced.
Q5: Are there limitations to this model?
A: This is a simplified model that assumes infinite potential walls and neglects relativistic effects and particle interactions.