What Does a 5 mW Green Laser Pointer Actually Send Out?

What comes out of the front of a green laser pointer? Light, obviously, but light is delivered in packets, and the numbers for those packets are strange. A pointer at the 5 mW limit that US laser pointers have to stay under, shining at 532 nm, sends out 1.339 × 10¹⁶ photons every second. Each one carries 2.331 eV. And not one of them can knock an electron out of a sodium surface, because each falls 419.470 meV short.

That is the whole answer in three numbers. The rest of this article takes it apart with the Wavelength to Color Calculator, the Wave Frequency Calculator and the Photon Energy Calculator, then asks what changes when the pointer is red or violet, when the metal is different, and when the wave is not light at all but a tuning fork or a Wi-Fi router. Every figure below came straight out of those calculators.

Where the three numbers come from

Start with the wavelength printed on the pointer, 532 nm, and everything else follows from constants that are exact by definition. Divide the speed of light by the wavelength and you get the frequency. Multiply the frequency by the Planck constant and you get the energy of one photon. Divide the power by that energy and you get the number of photons per second. The table walks through it in that order.

The last line matters for the sodium verdict. Brightness decides how many photons arrive; it does nothing to how much energy each one brings. The Wikipedia article on the photoelectric effect puts it plainly: more intensity raises the number of electrons ejected, not their kinetic energy. So the only question for sodium is whether a single 2.331 eV photon beats its work function of 2.75 eV. It does not, and turning the power up changes nothing.

The screenshot shows the longest wavelength that still works on sodium, 450.85 nm. That is blue-violet territory, which is where the next question points.

What if the pointer were a different color?

What if it were red?

A red pointer at 650 nm sends 1.636 × 10¹⁶ photons a second from the same 5 mW, more than the green one, because each photon is weaker: 1.907 eV. The ratio is exactly the ratio of the wavelengths, 650 to 532, or 1.2218. On sodium it is even further off than green, 842.551 meV short per photon. A 638 nm red pointer lands in between at 1.943 eV and 1.606 × 10¹⁶ photons a second.

What if it were violet?

Now the answer flips. A 405 nm pointer puts out fewer photons, 1.019 × 10¹⁶ a second, but each carries 3.061 eV, and that clears sodium's 2.75 eV. The fastest electrons leave with 311.338 meV. A blue 473 nm pointer is closer than green but still misses by 128.770 meV: 473 nm is longer than the 450.85 nm cutoff, and no amount of blue power can make up the difference.

What if the metal were caesium or potassium?

Keep the green pointer and change the surface. Caesium has the lowest work function in the table the calculator uses, 1.95 eV, so the same 2.331 eV photon frees electrons from it with 380.530 meV to spare, and any light shorter than 635.82 nm would do. Potassium, at 2.29 eV, only just gives way: the fastest electrons carry 40.530 meV, and the cutoff is 541.42 nm. Of the fourteen metals in the table, those two are the only ones green light can move; sodium, calcium, lithium and every other entry stay put.

What if the green were a shade closer to the eye's favorite?

Daylight vision is most sensitive at 555 nm. A 532 nm beam sits 23.00 nm short of that peak. Light at 552 nm, only 3.00 nm short, still reads as green, at 543.10 THz and 2.246 eV a photon, and the Wavelength to Color Calculator draws it as a yellower swatch, #a9ff00 against #65ff00 for 532 nm. Both are screen approximations; a monitor cannot show a single wavelength.

The table below runs the same arithmetic across the visible range. The color column opens the matching "what color is" page and the photon energy column opens the matching energy page, each with the wavelength already typed in.

What if the wave were not light?

What if it were a 440 Hz tuning fork?

The relation between speed, frequency and wavelength is the same for sound, just with a much slower speed. Concert A at 440 Hz in air at 20 °C, where sound travels at 343 m/s, has a wavelength of 77.95 cm, or 2.56 ft. Each cycle takes 2.27 ms. The green laser's light oscillates 1.2807 × 10¹² times as often, and its waves are 1.4652 × 10⁶ times shorter than the note's. Put the same fork under water and the wavelength stretches to 3.37 m; the pitch does not change, because the fork still sets the frequency.

Here are the wavelengths of ten tones in air. Each frequency opens its own page with air and hertz already set.

The lowest tone people hear, 20 Hz, has a wave 17.15 m long, exactly one hundred times the 17.15 cm of the 2,000 Hz tone. Divide the frequency by ten and the wavelength grows ten times.

What if it were Wi-Fi?

Radio is electromagnetic radiation too, only with far longer waves. A 2.4 GHz Wi-Fi signal has a wavelength of 12.49 cm, and each of its photons carries 9.926 µeV. The green pointer's photon is 2.348 × 10⁵ times more energetic. The same 5 mW from a 2.4 GHz source would therefore be 3.144 × 10²¹ photons a second, hundreds of thousands of times more than the laser, and every one of them far too weak to free an electron from anything in the metal table.

Wi-Fi uses 2.4 and 5 GHz, Wi-Fi 6E adds 6 GHz, and IEEE 802.11ad works at 60 GHz, according to Wikipedia's Wi-Fi article; 28 GHz sits inside 5G band n257, which runs from 26.50 to 29.50 GHz.

What if all you have is an energy in eV?

Physics problems often skip the wavelength and give the photon energy. The conversion runs the other way, 1239.84 divided by the electronvolts gives nanometers, and the Wavelength to Color Calculator names the band. Two electronvolts is orange light at 619.92 nm; four is already ultraviolet B.

Five sources at 5 mW, side by side

Same power, five very different beams. The photon count rises as each photon gets weaker, and only one row frees electrons from sodium.

So is five milliwatts a lot?

Counted in photons, yes: more than ten quadrillion every second. Counted per photon, hardly anything, and for the photoelectric effect the per-photon number is the only one that matters. For most everyday light the useful habit is to ask both questions separately, how many and how strong, because they answer different things, and a brighter beam only ever changes the first.

Tools discussed in this article

• Wavelength to Color Calculator: a wavelength, frequency or photon energy turned into the other two, the band of the spectrum and the color name
• Wave Frequency Calculator: v = f × λ for sound in air, water, tissue, granite, iron or diamond, with the period and the nearest piano key
• Photon Energy Calculator: photon energy in eV, joules and kJ/mol, photons per second from a power, and a photoelectric check against fourteen metals

More physics tools

The rest of the physics shelf, in the order it was built:

• Momentum Calculator, Force Calculator and Kinetic Energy Calculator
• Potential Energy Calculator, Work Calculator and Mechanical Power Calculator
• Torque Calculator, Kinetic Friction Calculator and Pendulum Period Calculator
• Thermal Expansion Calculator, Specific Heat Calculator and Thermal Conductivity Calculator
• Hooke's Law Calculator, Simple Harmonic Motion Calculator and Buoyancy Calculator
• Acceleration Formula Calculator, Density Calculator and Temperature Converter
• Thermal Efficiency Calculator, Gravitational Force Calculator and Snell's Law Calculator
• Refractive Index Calculator, Thin Lens Calculator and Magnifying Glass Calculator