The Electron Wavelength Calculator is an online tool designed to compute the wavelength of an electron using the principles of quantum mechanics, specifically the de Broglie hypothesis. This calculator simplifies the process of determining the electron's wavelength by automating the calculations that involve Planck's constant, the electron's mass, velocity, and kinetic energy.

## Formula of Electron Wavelength Calculator

The core of this calculator's functionality is based on the de Broglie wavelength formula, which connects quantum mechanics to classical physics. The formula is expressed as:

λ = h / p

Where:

`λ`

is the wavelength.`h`

is Planck's constant (6.626 x 10^-34 Joule seconds).`p`

is the momentum of the electron.

To find the momentum (`p`

) of an electron, it is calculated as:

p = m * v

Where:

`m`

is the mass of the electron (9.109 x 10^-31 kilograms).`v`

is the velocity of the electron.

Integrating these values, the wavelength (`λ`

) of an electron can also be derived from:

λ = h / (m * v)

For velocity derived from kinetic energy (E_k):

v = sqrt(2 * E_k / m)

Thus, substituting `v`

:

λ = h / sqrt(2 * m * E_k)

This final expression provides a direct method to compute the wavelength if the kinetic energy of the electron is known.

## Table of Common Values

Kinetic Energy (eV) | Electron Wavelength (nanometers) |
---|---|

1 | 1.227 |

10 | 0.388 |

50 | 0.174 |

100 | 0.123 |

500 | 0.055 |

1000 | 0.039 |

## Example of Electron Wavelength Calculator

**Problem:** Calculate the wavelength of an electron with a kinetic energy of 30 eV.

**Solution:**

- Identify the kinetic energy, E_k = 30 eV.
- Use the formula for wavelength in terms of kinetic energy:λ = h / sqrt(2 * m * E_k)Substituting the constants and value:
- h = 6.626 x 10^-34 Joule seconds
- m = 9.109 x 10^-31 kilograms
- E_k = 30 eV

## Most Common FAQs

**1. What is Planck's constant and why is it important in this calculation?**

Planck's constant is a fundamental quantity in quantum mechanics. It appears in the de Broglie wavelength formula and plays a critical role in determining the scale at which quantum mechanical effects become significant.

**2. How accurate is the Electron Wavelength Calculator?**

The accuracy of the calculator depends on the precision of the input values. It is design to provide results base on non-relativistic quantum mechanics, suitable for most educational and many professional applications.

**3. Can this calculator be use for relativistic speeds?**

The provided formula and calculator are optimize for non-relativistic speeds. For calculations involving near-light speeds, relativistic corrections would be necessary.