Understanding Planck's Constant in eV·s and Its Role in Quantum Physics.

Outline

• Opening: Planck’s constant as a bridge between energy and color, and why units matter.

• The question at hand: value of h in eV·s, with options and the right pick.

• What is Planck’s constant? E = hν and why h is central in quantum physics.

• Unit conversion basics: from J·s to eV·s, step by step.

• The math in plain terms: deriving h in eV·s and what the number means.

• Quick checks: why the other options don’t fit.

• Real-world flavor: photons, spectra, and the photoelectric effect—how h guides these ideas.

• Practical tips: how to keep units straight in quantum relations.

• Final note: the big picture of Planck’s constant and its role in modern physics.

Planck’s constant, plain and simple

Imagine you have a tiny tuning knob that links energy to color. That knob is Planck’s constant, h. In quantum physics, many relationships hinge on it, but the most famous is E = hν, where E is energy and ν (nu) is frequency. If you want energy tied to a photon’s color, you’ll reach for h. It’s one of those constants you encounter again and again—like meeting a guide who never tires of explaining how light and matter talk to each other.

The question and the right answer

If you’re looking at a typical multiple-choice setup, you’ll see values in different units. The correct one for h when expressed as energy per time in electronvolts becomes:

h ≈ 4.1357 × 10⁻¹⁵ eV·s

Option C matches this value exactly.

A quick sanity check: where does this come from?

• We start with the more familiar h in joule-seconds: h = 6.62607015 × 10⁻³⁴ J·s.

• We also know the conversion between joules and electronvolts: 1 eV = 1.602176634 × 10⁻¹⁹ J.

• To convert h to eV·s, divide by the joules-to-eV factor:

h (eV·s) = h (J·s) / (1.602176634 × 10⁻¹⁹ J/eV)

h (eV·s) ≈ 6.62607015 × 10⁻³⁴ / 1.602176634 × 10⁻¹⁹

h (eV·s) ≈ 4.135667696 × 10⁻¹⁵ eV·s.

Rounding gives about 4.1357 × 10⁻¹⁵ eV·s, which is exactly the value in option C.

Let’s unpack why this matters, in terms you can actually use

• E = hν is the bridge between what a photon’s energy is and how fast its wave oscillates. If a photon has a frequency of 1 Hz, the energy is h × 1 Hz, which is 4.1357 × 10⁻¹⁵ eV. If the frequency is higher, energy scales directly with ν.

• In practice, this relationship helps explain the photoelectric effect: only photons with enough energy (E ≥ φ, the work function) can liberate electrons. The higher the frequency, the more energy each photon carries, even if the color looks similar to the eye.

• In atomic spectra, the lines we see are the fingerprints of transitions between energy levels. The energy difference ΔE between levels relates to frequency via ΔE = hν, so Planck’s constant is the translator between color and energy.

A closer look at the unit conversion

If you want to become fluent with units, this is a handy routine:

• Remember the core numbers: h_Js ≈ 6.626 × 10⁻³⁴ J·s and 1 eV ≈ 1.602 × 10⁻¹⁹ J.

• To convert h to eV·s, divide by the J-to-eV conversion factor.

• The result tells you how much energy, in electronvolts, corresponds to a photon oscillating at 1 Hz.

This is the kind of mental math that saves you from getting tangled when you tackle problems about photons, spectra, or photoemission.

Where the other options misfire

Let’s do a quick fact-check on the distractors, just to sharpen intuition:

• A: 6.626 × 10⁻³⁴ eV·s. Here the exponent looks right, but the unit inside is off. h in eV·s should include the eV factor; you can’t drop the conversion from joules to electronvolts and call it a day.

• B: 1.6 × 10⁻¹⁹ eV·s. This is the rough size of 1 electronvolt in joules, not Planck’s constant. It’s a classic confusion between the energy unit and the constant that links energy to frequency.

• D: 3 × 10⁸ eV·s. That’s a playful nod to the speed of light (roughly 3 × 10⁸ m/s), not a unit for Planck’s constant. It’s a reminder to keep straight what a number is measuring.

By keeping the logic clean—B is energy, D is a speed—you're less likely to slip into mix-ups when you’re solving problems.

A real-world feel: photons, spectra, and the world around us

Think about a rainbow of light: sunlight, a lamp, a laser. Each color corresponds to a different frequency. When that light interacts with matter, energy transfer follows rules tied to h. In the photoelectric effect, you need photons energetic enough to knock electrons free. In hydrogen’s emission spectrum, electrons jump between levels, emitting photons with precise energies. In laser physics, the emitted photons are born from precise energy gaps, a direct nod to E = hν.

All these scenarios hinge on a single, compact statement: energy is proportional to frequency with Planck’s constant as the proportionality factor. That tiny constant sets the scale for quantum effects. And yes, the scale is tiny—because quantum actions are subtle at everyday energy levels—but it’s exactly this scale that makes atoms, photons, and all the strange beauty of quantum phenomena possible.

Tips for keeping the ideas clear (without getting lost in the symbols)

• Use E = hν as your first checkpoint. If you know the frequency, you can find the energy, and vice versa.

• Always watch the units. If you start in joules, convert to electronvolts only when needed, and keep track of the exponent. It’s easy to trip on a 10⁻¹⁵ here and a 10⁻¹⁹ there.

• When you see a problem with photons or spectra, sketch a quick diagram: a photon with energy E, a frequency ν, and the relation E = hν. Seeing the connections visually helps.

• Don’t panic over tiny numbers. Physics loves powers of ten. They’re not random; they’re a language for scale. 10⁻¹⁵ and 10⁻¹⁹ are just two notes in the same melody.

• If a value doesn’t feel right, do a quick dimensional check. Units guide intuition as surely as numbers do.

A little more texture: why this constant matters beyond one question

Planck’s constant is a building block of quantum mechanics. It appears in wave-particle duality, uncertainty principles, and even in modern technologies like LEDs and solar cells. The same h that links energy to frequency also underpins the way electrons inhabit atoms, how lasers function, and how we describe the tiniest interactions of light with matter. That’s the grand arc: a single constant shaping the behavior of nature across scales, from the glow of a glowstick to the keystone equations behind quantum computers.

Putting it together: what to take away

• The value of Planck’s constant in eV·s is about 4.1357 × 10⁻¹⁵ eV·s.

• This comes from converting the standard h (in J·s) to eV·s using the conversion 1 eV = 1.602176634 × 10⁻¹⁹ J.

• The right answer among common choices is C. The other options either misplace the unit or mix up a different physical quantity entirely.

• In practice, remember E = hν as the quick link between energy and frequency, and use careful unit tracking to keep your work clean.

Final thought

Next time you stare at a spectrum or think about a photon’s energy, let Planck’s constant be your guide. It’s a quiet, constant companion that quietly tells you how the universe tunes its own music. And that’s a pretty elegant thing to carry in your pocket as you explore the quantum world. If you keep that analogy in mind, you’ll find yourself navigating these ideas with a bit more curiosity and a lot more confidence.