Here's how to find the frequency of light with a 500 nm wavelength.

Light travels, but frequency has a voice. When you know the wavelength of light, you can hear that voice loud and clear—the frequency. For many chemistry topics, that number isn’t just trivia; it connects to energy, color, and how we read spectra in the lab. Let’s walk through a clean, practical way to get from a wavelength to a frequency, using a neat, real-world example you might bump into in SDSU-style chemistry discussions.

The core idea: c = λν

• c is the speed of light, about 3.0 × 10^8 meters per second.

• λ (lambda) is the wavelength in meters.

• ν (nu) is the frequency in hertz (cycles per second).

If the wavelength is 500 nanometers, what’s the frequency?

Let me explain with a simple, no-frills calculation. It helps to see every step, because tiny slips in units or exponent tricks can derail you fast.

Step 1: Convert the wavelength to meters

• 500 nm = 500 × 10^-9 m = 5.0 × 10^-7 m

Step 2: Solve for frequency

• ν = c / λ

• ν = (3.0 × 10^8 m/s) / (5.0 × 10^-7 m)

Step 3: Do the math

• Divide the numbers: 3.0 / 5.0 = 0.6

• Handle the powers: 10^8 / 10^-7 = 10^(8 + 7) = 10^15

• Put it together: ν = 0.6 × 10^15 Hz = 6.0 × 10^14 Hz

So the frequency is 6.0 × 10^14 Hz.

If you like a quick check: this falls right in the visible spectrum, around green light. The visible spectrum itself spans roughly 4.0 × 10^14 to 7.5 × 10^14 Hz, so 6.0 × 10^14 Hz is solidly in the middle. Seeing these numbers link to color is one of those moments where math and color perception click together.

Why this matters beyond a plug-in formula

• Photons carry energy. The energy of a photon relates to frequency via E = hν, where h is Planck’s constant (6.626 × 10^-34 J·s). If ν = 6.0 × 10^14 Hz, then E ≈ (6.626 × 10^-34 J·s) × (6.0 × 10^14 s^-1) ≈ 3.98 × 10^-19 J per photon. In electronvolts, that’s about 2.48 eV (since 1 eV = 1.602 × 10^-19 J). That’s the tidy energy scale you’ll see when you talk about absorbing or emitting green light in a chemical system.

• The same relationship links spectroscopy, color, and reactions. If a sample absorbs light at a certain wavelength, it’s absorbing photons with a particular energy, and that energy can drive or suppress specific electronic transitions.

A quick map to color and chemistry

• Green light at 500 nm (roughly 6.0 × 10^14 Hz) sits in a sweet spot for many organic and inorganic transitions. It’s not too high energy, not too low. That makes it a handy reference point when you’re thinking about d-d transitions in transition metals or π–π* transitions in organic chromophores.

• In practical lab work, you’ll often see LEDs or lamps emitting in bands around this wavelength. If you’re running a UV–Vis spectrometer, you’ll be translating the light you send through a sample into a spectrum that reveals which wavelengths get absorbed—and thus which transitions are active.

A few handy reminders to keep you sharp

• Units matter. The first thing to check is that you’ve got wavelength in meters (not nanometers) when you plug into c = λν.

• Watch the exponents. A small slip with powers of ten is a classic rookie mistake. When you convert nanometers to meters, you’re shifting decimal places by 9 powers of ten.

• Keep the concept in sight. This is a frequency–energy bridge. Frequency tells you how fast the wave oscillates; energy tells you what the photon can do to a molecule. Both are two sides of the same coin.

A tiny detour you might appreciate

• If you’re curious about the flip side, you can also start from wavelength to get photon energy and then relate that to chemical behavior. Once you know E = hc/λ, you can connect how changing λ shifts energy and changes whether a molecule can promote an electron from a ground state to an excited state. In real life, that’s how color chemistry and light-driven reactions get explained.

Common places where it trips people up (so you don’t stumble)

• Forgetting to convert nm to m. It’s easy to leave the wavelength in nm and still expect a sensible ν. It doesn’t work that way—the units must line up.

• Skipping the step where you separate numbers from exponents. Your brain might handle 3.0 and 5.0, but the exponent arithmetic is where the error often slips in.

• Framing frequency like a speed limit or a rate in a weird way. Frequency is simply cycles per second; energy and color come from tying that to Planck’s constant and the wavelength.

A real-world aside you’ll carry into the lab

• In spectroscopy labs, students love plotting absorbance versus wavelength. The peak where absorbance is strongest corresponds to photons that the sample uses to jump to a higher energy level. If your sample absorbs at 500 nm, you’ve basically tuned it to drink in those 6.0 × 10^14 Hz photons. It’s a practical reminder that light isn’t just something you measure; it’s something you interact with at a molecular level.

A little quiz moment (because a question in context helps)

Question: What is the frequency of light with a wavelength of 500 nm?

A. 3.0 × 10^14 Hz

B. 6.0 × 10^14 Hz

C. 7.5 × 10^14 Hz

D. 1.0 × 10^14 Hz

The correct answer is B, 6.0 × 10^14 Hz. Here’s why, in a nutshell:

• Convert 500 nm to meters: 500 × 10^-9 m = 5.0 × 10^-7 m

• Apply c = λν: ν = c/λ = (3.0 × 10^8) / (5.0 × 10^-7) = 6.0 × 10^14 Hz

• Quick sanity check: 500 nm sits near green, consistent with a frequency around 6 × 10^14 Hz, well inside the visible window.

Connecting the dots

If you’re exploring chemistry here in sunny California or anywhere else, this relationship is a friendly anchor. It keeps sense-making grounded when you’re analyzing spectra, predicting what colors a compound might absorb, or just talking about photons in a lab notebook. The math is straightforward, but the implications are surprisingly broad—from how LEDs light up our rooms to how researchers understand photosynthesis in plants.

To wrap up, the path from wavelength to frequency isn’t a parade of abstract symbols. It’s a compact, practical tool that helps you read light as if it’s giving you a message about energy, color, and matter. With a little practice, you’ll flip between wavelength, frequency, and energy in a heartbeat, and you’ll feel that satisfying click when the numbers line up with what you observe in real experiments.

If you want, we can walk through a few more examples together—start with a common visible-wavelength value, and we’ll translate it into frequency, then energy, and even connect it to a sample’s color. It’s the kind of tiny workout that makes the lab notebook feel less intimidating and more like a conversation with light itself.