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Electromagnetism & Quantum Optics
Photon Energy & Quantum Efficiency Calculator
Instantly compute photon energy, flux, irradiance, and photochemical reaction rate from wavelength, source power, beam area, and quantum yield. Covers the full UV–IR spectrum.
Parameters
Wavelength λ
nm
Source Power P
mW
Beam Area A
cm²
Source Type
Quantum Yield Φ
Irradiation Time t
s
Results
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Photon Energy E (eV)
—
Frequency ν (THz)
—
Photon Flux (ph/s/cm²)
—
Irradiance (mW/cm²)
—
Molar Photons (μE/s)
—
Reaction Rate (nmol/s)
Photon Energy vs Wavelength (UV–IR)
Photon Flux vs Wavelength (at current power P)
Theory & Key Formulas
$$E = \frac{hc}{\lambda}= h\nu$$
$h = 6.626\times10^{-34}$ J·s
$c = 2.998\times10^8$ m/s
Photon Flux:
$$\Phi_p = \frac{P \cdot \lambda}{h c A}$$
Molar Photon Rate:
$$n_p = \frac{P \cdot \lambda}{h c N_A}$$
What is Photon Energy & Quantum Efficiency?
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What exactly is "photon energy"? I know light has energy, but what does this calculator tell me?
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Basically, it tells you the energy carried by a single particle of light (a photon) at a specific color, or wavelength. The core idea is that blue light packs more energy per photon than red light. In the simulator, try moving the Wavelength slider from the red end (700 nm) to the blue end (400 nm). You'll see the photon energy in electronvolts (eV) increase instantly.
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Wait, really? So if I have a laser pointer, how many photons are coming out per second? Is that the "flux"?
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Exactly! That's the photon flux – the number of photons hitting an area each second. It depends on the laser's power, its color, and the beam size. For instance, a common 5 mW green laser pointer has a huge number of photons per second. In the simulator, set a low power and a small area, then watch the flux value. Now increase the Power slider; see how the flux skyrockets? That's the relationship you're calculating.
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Okay, I get energy and flux. But what's the point of the "Quantum Yield" selector? That sounds like chemistry.
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Great question! It bridges physics and chemistry. Quantum Yield tells you what fraction of incoming photons actually causes a useful reaction, like exciting a molecule in a solar cell or triggering a sensor. A yield of 1.0 means every photon counts; 0.5 means half are wasted. Change the Quantum Yield selector in the tool. You'll see the final "Reaction Rate" change directly. This is the key number for designing efficient photochemical processes.
Physical Model & Key Equations
The fundamental relationship between a photon's energy (E) and its wavelength (λ) or frequency (ν) is given by Planck's equation. This tells us that shorter wavelengths (bluer light) correspond to higher energy photons.
$$E = \frac{hc}{\lambda}= h\nu$$
$E$ = Photon energy (Joules). $h$ = Planck's constant ($6.626 \times 10^{-34}$ J·s). $c$ = Speed of light ($2.998 \times 10^8$ m/s). $\lambda$ = Wavelength (m). $\nu$ = Frequency (Hz).
To find out how many of these photons are delivered by a light source, we calculate the photon flux (Φₚ). This is the number of photons per second per unit area, derived from the total optical power (P) spread over an area (A).
$$\Phi_p = \frac{P \cdot \lambda}{h c A}$$
$\Phi_p$ = Photon flux (photons·s⁻¹·m⁻²). $P$ = Total radiant power (Watts). $A$ = Illuminated area (m²). The product $\Phi_p \times A$ gives the total photons per second.
Frequently Asked Questions
Please enter the wavelength in meters (m). However, the tool does not have a function to automatically convert to nm (nanometers) or μm (micrometers), so for example, for 500 nm, you need to enter "500e-9".
Quantum yield is the probability that a desired reaction (e.g., electron-hole pair generation or chemical reaction) occurs when one photon is absorbed. Set it within a range of 0 to 1. For example, for solar cells, it is typically 0.8 to 1.0, and for photocatalysts, it is generally around 0.01 to 0.1.
Irradiance (unit: W/m²) is the amount of light energy per unit area, a physical quantity that does not consider human eye sensitivity. Photon flux (unit: photons/s/m²) is the number of photons arriving per unit area per unit time. The shorter the wavelength, the fewer photons there are for the same energy.
Yes, it is possible. However, lasers are typically single-wavelength and high-brightness, so please set the irradiation area correctly. If the beam diameter is small, entering a small area is necessary; otherwise, the irradiance will be calculated as lower than actual. For pulsed lasers, use the average output.
Real-World Applications
Solar Cell Design: Engineers use these calculations to predict the maximum possible current a solar cell can generate. By knowing the photon flux from the sun at different wavelengths and the material's quantum yield (here called external quantum efficiency), they can model and optimize cell efficiency before fabrication.
Photochemical Reactors: In industrial chemistry driven by light, such as water purification or pharmaceutical synthesis, the reaction rate is directly proportional to the absorbed photon flux. Precise calculation of photon delivery ensures the process is efficient, scalable, and cost-effective.
Biological & Medical Sensing: Techniques like fluorescence microscopy or photodynamic therapy rely on molecules absorbing a specific number of photons to emit light or produce a therapeutic effect. Calculating the local photon flux is critical for determining dosage and imaging sensitivity.
Optical Communications: In fiber optics, data is sent as pulses of light. The number of photons per pulse determines the signal strength and the likelihood of error at the receiver. These calculations are fundamental for designing low-power, high-bandwidth communication systems.
Common Misunderstandings and Points to Note
There are a few key points I want you to be especially mindful of when starting to use this tool. First, "the source output power P is not necessarily the total energy reaching the irradiated surface." For example, even if an LED datasheet states "radiant flux 1W," there are losses in the lens or optical system, as well as reflection losses due to the angle of incidence on the surface. In practice, you need to estimate this "optical efficiency" and correct the P value you input into the tool. For instance, if the optical system's transmittance is 80%, you should calculate using an effective P of 0.8W.
Next is the point that "the photon flux is not uniform." The tool gives you a value averaged over the irradiated area A, but an actual laser beam has a Gaussian distribution, and LED light isn't uniform either. To precisely estimate reaction rates, you need to consider the flux distribution across the area. It's entirely possible for the reaction rate at the center to be ten times different from that at the edges.
Finally, a super important fact: "quantum efficiency is wavelength-dependent." While you set a single value in the tool, the actual quantum efficiency of a photocatalyst or solar cell can vary greatly with wavelength. It's common to have 50% at 450nm blue light but only 10% at 650nm red light. Therefore, the "reaction rate calculated for this wavelength" is strictly for that monochromatic light. When using broad-spectrum sunlight, you need to integrate the calculation results for each wavelength.