Energy Of Particle In Ny Level In 3D Box Calculator

Energy of Particle in Box along Y axis Formula:

\[ E_y = \frac{(n_y)^2 \times (h)^2}{8 \times m \times (l_y)^2} \]

Energy of Particle in Box along Y axis:

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1. What is Energy of Particle in Box along Y axis?

Energy of Particle in Box along Y axis is defined as the energy values that a particle can have residing in one level in a quantum mechanical system where the particle is confined to a box along the Y-axis.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ E_y = \frac{(n_y)^2 \times (h)^2}{8 \times m \times (l_y)^2} \]

Where:

\( E_y \) — Energy of Particle in Box along Y axis (J)
\( n_y \) — Energy Levels along Y axis (unitless)
\( h \) — Planck's constant (6.626070040 × 10^-34 J·s)
\( m \) — Mass of Particle (kg)
\( l_y \) — Length of Box along Y axis (m)

Explanation: This formula calculates the quantized energy levels of a particle confined to a one-dimensional box along the Y-axis, derived from solving the Schrödinger equation for this system.

3. Importance of Energy Calculation

Details: Calculating the energy of a particle in a box is fundamental in quantum mechanics and helps understand quantized energy states, which are important in various fields including nanotechnology, semiconductor physics, and quantum chemistry.

4. Using the Calculator

Tips: Enter the quantum number (n_y), mass of the particle in kilograms, and length of the box along Y-axis in meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What does the quantum number n_y represent?
A: The quantum number n_y represents the energy level of the particle along the Y-axis and must be a positive integer (1, 2, 3, ...).

Q2: Why is the energy quantized in this system?
A: The energy is quantized because the particle is confined to a finite region, and the wavefunction must satisfy boundary conditions at the walls of the box.

Q3: What are typical values for mass and length in these calculations?
A: For atomic-scale systems, mass is typically on the order of 10^-30 to 10^-27 kg (electron to atom mass), and length is typically on the order of 10^-10 m (atomic scale).

Q4: Can this formula be used for macroscopic objects?
A: While the formula is theoretically valid, the energy quantization is negligible for macroscopic objects due to their large mass and size compared to quantum scales.

Q5: How does this relate to the 3D particle in a box problem?
A: This calculation is for one dimension (Y-axis) of a 3D box. The total energy in a 3D box would be the sum of energies along all three dimensions.