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Wavelength to Energy Calculator

The wavelength to energy formula – Planck's equationHow do I calculate energy from wavelength?More wavelength and energy calculators!FAQs

This is Omni's wavelength to energy calculator, a tool that instantly calculates a photon's energy from its wavelength. By using Planck's equation, this tool will help you determine a photon's energy in joules (J), electronvolts (eV), or its multiples.

In this article, you'll also find the Planck equation, a step-by-step guide on how to calculate the energy from the wavelength of a photon and how to get this result in joules or electronvolts.

The wavelength to energy formula – Planck's equation

Planck's equation, also known as Planck's relation, is an expression that allows you to define a photon's energy E in terms of its wave properties. Planck's relation states that the energy is directly proportional to its frequency $f$:

$E = h \cdot f$

Or inversely proportional to wavelength $\lambda$, by recalling the relationship between frequency and wavelength, $f = c / \lambda$:

$E = \dfrac {h \cdot c}{\lambda}$

where:

• $E$ — Photon energy;
• $h$ — Planck's constant, 6.6261 × 10⁻³⁴ J⋅s or 4.1357 × 10⁻¹⁵ eV⋅s;
• $c$ — Speed of light, 299792458 m/s;
• $\lambda$ — Wavelength; and
• $f$ — Photon frequency.

Notice that if a photon's frequency $f$ or wavelength $\lambda$ are known, you can directly determine its energy $E$ since the other elements in the equation are constants.

🙋 The energy of a photon is commonly expressed using the unit electronvolt (eV), but it can also be expressed in other energy units, such as joules (J).

How do I calculate energy from wavelength?

To calculate a photon's energy from its wavelength:

1. Multiply Planck's constant, 6.6261 × 10⁻³⁴ J⋅s by the speed of light, 299,792,458 m/s.
2. Divide this resulting number by your wavelength in meters.
3. The result is the photon's energy in joules.

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FAQs

How do I find the energy in joules given the wavelength?

To find the energy in joules given the wavelength of a photon:

1. Use Planck's equation E = h × c / λ and substitute the values of the wavelength (λ), Planck's constant in joules (h = 6.6261 × 10⁻³⁴ J⋅s), and speed of light (c = 299792458 m/s).
2. With these units, you'll get an energy result in joules (J).
3. That's it!

How do I convert wavelength to energy in eV?

In order to convert a wavelength to energy in electronvolts (eV):

1. Utilize Planck's energy equation E = h × c / λ.

2. Substitute the values of the wavelength (λ), Planck's constant (h = 6.6261 × 10⁻³⁴ J⋅s), and speed of light (c = 299792458 m/s).

3. You'll get a result in joules (J).

4. To go from joules (J) to electronvolts (eV), use the conversion factor 1 eV = 1.602176565 × 10⁻¹⁹ J.

5. Finally, to express your result in electronvolts, divide the energy in joules by the conversion factor:

E [J] / 1.602176565 e⁻¹⁹ J/eV = E [eV]

How do I calculate the energy of a photon of wavelength 3.5 μm?

To calculate the energy of a photon of wavelength 3.5 μm:

1. Employ Planck's energy equation, E = h × c / λ.

2. Use the values of the wavelength λ = 3.5 μm, Planck's constant h = 6.6261 × 10⁻³⁴ J⋅s and speed of light c = 299792458 m/s.

3. Substitute into Planck's equation, E = 3.5 μm × (6.6261 × 10⁻³⁴ J⋅s) × (299792458 m/s).

4. After performing the required operations, you'll get the energy value E = 354.242 meV.

What is the energy of a 100 nm photon?

The energy of a 100 nm photon is 12.39847 eV or 1.99 × 10⁻¹⁸ J. To get this result:

1. Employ Planck's equation:

E = h × c / λ

where λ = 3.5 μm is the wavelength, h = 6.6261 × 10⁻³⁴ J⋅s Planck's constant and c = 299792458 m/s the speed of light.

2. Replace, E = 3.5 μm × (6.6261 × 10⁻³⁴ J⋅s) × (299792458 m/s) = 12.39847 eV.

3. To express the result in joules, apply the conversion factor 1eV = 1.602176565 × 10⁻¹⁹ J. Therefore:

E = 12.39847 eV × (1.602176565 × 10⁻¹⁹ J/eV) = 1.99 × 10⁻¹⁸ J