# Electron Energy Calculator

*Created by Team y2calculate.com*

Content written by Jangir khan (Ph.D.)

Calculator code by Marcelino

Reviewed by Hezbollah (Ph.D.)

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#### Table of Contents

## What is energy of electron?

The energy of an electron refers to the total energy possessed by an electron in its particular energy state within an atom. In the context of atomic physics, an electron’s energy is a combination of its kinetic energy (associated with its motion) and potential energy (associated with its position in relation to the atomic nucleus). given formula can be use to calculate electron energy in orbit

${\mathrm{En}}_{}=-\frac{1312.36\text{\hspace{0.17em}}\text{}{\mathrm{n$ \frac{{\mathrm{}}^{}}{}$2}}^{}}{}$ $\frac{\text{Kj}\text{}}{}$$\frac{{\mathrm{per\; mole}}^{}}{}$

The energy levels of electrons in an atom are quantized, meaning they exist in distinct, allowable energy states or shells. The energy of an electron in a specific shell is determined by the quantum number associated with that shell. The lower the shell number, the lower the energy level of the electron.

## Formula for calculating energy of electron

The formula for calculating the energy of an electron in a hydrogen-like atom is given by the following expression:

${\mathrm{En}}_{}=-\frac{13.6\text{\hspace{0.17em}}\text{eV}}{{$ {n}_{}$}^{2}}$

where:

- ${}_{}$ is the energy of the electron in the $$-th energy level,
- $$ is the principal quantum number of the energy level.

This formula is derived from the Bohr model of the hydrogen atom and represents the quantized energy levels that electrons can occupy in an atom. The negative sign indicates that the electron is bound to the nucleus, and the energy is lower for electrons in lower energy levels (closer to the nucleus) and higher for electrons in higher energy levels (farther from the nucleus). The energy is typically expressed in electron volts (eV).

## why energy of electron in orbit is quantize?

The quantization of electron energy in orbit is a fundamental concept in quantum mechanics, and it is primarily explained by the Bohr model of the hydrogen atom, proposed by Niels Bohr in 1913. Here are the key reasons why the energy of an electron in orbit is quantized:

**Standing Wave Nature:**- Electrons exhibit both particle and wave-like characteristics. In the Bohr model, electrons are considered as standing waves.
- Standing waves can only exist at specific frequencies (wavelengths) that fulfill certain conditions. Only certain orbits, corresponding to specific wavelengths, are allowed for electrons.

**Angular Momentum Quantization:**- Bohr proposed that the angular momentum of an electron in orbit is quantized and is an integral multiple of Planck’s constant divided by $2π$.
- Mathematically, this is expressed as $\mathrm{$ \frac{\mathrm{mvr}}{}$}=\frac{\mathrm{n\u210e}}{2\mathrm{\$\pi \$}}$
- $\frac{\mathrm{where\; the\; mass\; of\; the\; electron,\; v\; is\; its\; velocity,\; r\; is\; the\; radius\; of\; the\; orbit,\; n}}{}$$\mathrm{is\; an\; integer\; (quantum\; number),\; and\$h\$is\; Planck\u2019s\; constant.}$
- This condition leads to the quantization of the allowed orbits.

**Quantization of Energy Levels:**- The quantization of angular momentum implies the quantization of energy levels. Bohr related the electron’s energy to its orbit through the equation ${\mathrm{En}}_{}=-\frac{13.6\text{\hspace{0.17em}}\text{eV}}{{n}^{2}}$
- where $n$ is the principal quantum number.
- Electrons can only exist in orbits with specific energy levels corresponding to integer values of $n$.

**Wave-Particle Duality:**- Quantum mechanics recognizes the wave-particle duality of particles, where electrons, despite being particles, exhibit wave-like behavior.
- Only certain stable orbits allow the electron’s de Broglie wavelength to fit evenly into a complete orbit, reinforcing the concept of quantized energy.

In summary, the quantization of electron energy in orbit arises from the wave nature of electrons, the quantization of angular momentum, and the specific conditions that allow stable standing waves. This concept laid the foundation for the development of quantum mechanics and our understanding of the behavior of particles at the atomic and subatomic levels.