1. What is the Energy to Wavelength and Frequency Calculator?

Definition: This calculator converts photon energy ($E$) to wavelength ($\lambda$) and frequency ($f$) using the Planck-Einstein relation and wave speed equation.

Purpose: It is used in physics and optics to analyze the properties of light, such as in spectroscopy, quantum mechanics, and photonics.

2. How Does the Calculator Work?

The calculator uses the following formulas:

$f=\frac{E}{h}$

$\lambda =\frac{h\times c}{E}$

Where:

• $E$: Photon energy (J, eV, keV, MeV);
• $h$: Planck’s constant ($6.62607015\times {10}^{-34}{\text{J·Hz}}^{-1}$);
• $c$: Speed of light ($299792458\text{m/s}$);
• $f$: Frequency (Hz, kHz, MHz, GHz, THz);
• $\lambda$: Wavelength (m, nm, μm, mm, Å).

Steps:

• Enter the photon energy ($E$) with its unit.
• Convert the energy to Joules.
• Calculate the frequency using $f=\frac{E}{h}$.
• Calculate the wavelength using $\lambda =\frac{h\times c}{E}$.
• Convert the wavelength and frequency to the selected output units.
• Display the results, formatted in scientific notation if the absolute value is less than 0.001, otherwise with 4 decimal places.

3. Importance of Energy to Wavelength and Frequency Calculation

Calculating wavelength and frequency from energy is crucial for:

• Quantum Physics: Understanding photon properties.
• Spectroscopy: Analyzing light spectra.
• Optics: Designing lasers and optical systems.

4. Using the Calculator

Example 1: Calculate the wavelength and frequency for a photon with energy 2 eV:

• Energy: $E=2\text{eV}\times 1.60217662\times {10}^{-19}=3.20435324\times {10}^{-19}\text{J}$;
• Frequency: $f=\frac{E}{h}=\frac{3.20435324\times {10}^{-19}}{6.62607015\times {10}^{-34}}\approx 4.835\times {10}^{14}\text{Hz}$;
• Wavelength: $\lambda =\frac{h\times c}{E}=\frac{6.62607015\times {10}^{-34}\times 299792458}{3.20435324\times {10}^{-19}}\approx 6.198\times {10}^{-7}\text{m}$;
• Result (Wavelength in nm): $\lambda =619.8000\text{nm}$;
• Result (Frequency in Hz): $f=4.8350\times {10}^{14}\text{Hz}$.

Example 2: Calculate the wavelength and frequency for a photon with energy 1 MeV:

• Energy: $E=1\text{MeV}\times 1.60217662\times {10}^{-13}=1.60217662\times {10}^{-13}\text{J}$;
• Frequency: $f=\frac{E}{h}=\frac{1.60217662\times {10}^{-13}}{6.62607015\times {10}^{-34}}\approx 2.417\times {10}^{20}\text{Hz}$;
• Wavelength: $\lambda =\frac{h\times c}{E}=\frac{6.62607015\times {10}^{-34}\times 299792458}{1.60217662\times {10}^{-13}}\approx 1.239\times {10}^{-12}\text{m}$;
• Result (Wavelength in Å): $\lambda =12.3900\text{Å}$;
• Result (Frequency in THz): $f=241.7000\text{THz}$.

5. Frequently Asked Questions (FAQ)

Q: What is the Planck-Einstein relation?
A: It states that $E=h\times f$, where the energy of a photon is proportional to its frequency.

Q: Why use different units for energy?
A: Different fields use different energy units; for example, particle physics often uses eV, while general physics uses Joules.

Q: Does this calculator account for the medium?
A: No, this calculator assumes the speed of light in a vacuum ($c$). In other media, the speed of light changes, affecting the wavelength.

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