Energy of particle in a box

The Energy of a Particle in a Box calculator compute the energy of a particle in a box based on the energy level, mass of the particle and the length of the box.

INSTRUCTIONS: Choose units and enter the following:

• (n) Energy Level
• (m) Mass of Particle
• (L) Length of Box

Energy of a Particle in a Box(E_n): The calculator returns the energy in electron volts(eV).  However, this can be automatically converted to compatible units via the pull-down menu.

The Math / Science

The Energy of a particle in a box is found using the particle in a box model which describes a particle free to move in a small space surrounded by impenetrable barriers. The model is mainly used as a a hypothetical example to illustrate the differences between classical and quantum systems. The energy is found using the following formula:

     `E_n=(n^2h^2)/(8mL^2)`

where:

• E_n = Energy in a Box
• n = Energy level
• h = Planck's constant
• m = mass of particle
• L = Length of the box

Energy Calculators

• Kinetic Energy:                                    `KE= 1/2 *m * v^2`
• Kinetic Energy (change of velocity):    `KE = 1/2*m*(V_1-V_2)^2`
• Relativistic Kinetic Energy:                    `E_K = (m*c^2)/sqrt(1 - v^2"/"c^2") - m*c^2`
• Potential Energy:                                  `U(y) = m*g*y`
• Potential Energy of Gravity (two bodies):   `U(G) = - (G*m1*m2)/r`
• Nuclear Binding Energy:                       `E = m*c^2`
• Quantum Energy (Planck's Equation):   `E = h*f`
• Energy of a Particle in a Box:                `E_n=(n^2h^2)/(8mL^2)`
• Molecular Kinetic Energy:                      `KE = 3/2 * k_B *T`
• Electrostatic Potential Energy:               `E_(el) = k_e * (Q_1*Q_2)/d`
• Photon Energy from Wavelength:          `E = (h*c)/lambda`
• Heat Energy to Change Material Temperature:  `Q = C * m *DeltaT`

References

The formula and definition are from Wikipedia (https://en.wikipedia.org/wiki/Particle_in_a_box).