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(En): 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:
- En = 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).