Partícula na caixa - Energia
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
E_n = n²h²/(8mL²)
About this calculator
The Particle in a Box - Energy calculator is an online tool that allows you to calculate the energy of a particle confined in a one-dimensional box. The energy is calculated based on the formula E_n = n²h²/(8mL²), where n is a positive integer (n=1, 2, 3, ...), h is the Planck constant, m is the particle mass, and L is the box length.
The formula used is derived from the Schrödinger equation, which is a fundamental equation in quantum mechanics. The solution to the particle in a box is a classic example of how quantum mechanics can be applied to simple systems. The energy of the particle is quantized, meaning it can only take on specific discrete values.
This calculator is useful for students and professionals in chemistry and physics who need to calculate the energy of particles in different situations. For example, it can be used to study the energy of electrons in atoms or molecules, or to understand how the energy of a particle changes when the box length is altered.
When using this calculator, it's essential to be mindful of the units used for the variables. The Planck constant (h) is usually expressed in units of J s, the mass (m) in kg, and the length (L) in m. Ensure that the units are correct to obtain accurate results.
Frequently asked questions
What is the particle in a box?
The particle in a box is a theoretical model used in quantum mechanics to study the behavior of particles confined in a limited space.
How is the particle energy calculated?
The energy is calculated based on the formula E_n = n²h²/(8mL²), where n is a positive integer, h is the Planck constant, m is the particle mass, and L is the box length.
What are the units used in the formula?
The units used are: h (J s), m (kg), and L (m).
Can I use this calculator to study the energy of electrons in atoms?
Yes, this calculator can be used to study the energy of electrons in atoms or molecules, as long as the variables are adjusted correctly.
What if I don't know the value of a variable?
If you don't know the value of a variable, it's recommended to consult a reliable source or perform an experimental measurement to obtain the correct value.