Austin Peay State University · Physics Lab

The Spectrometer

Interactive lab-prep assistant — theory, Balmer-series predictor, and live data tables.

★Start here · How to use this page

This page is your phone-friendly companion to the lab worksheet. Use it tonight to prepare, and bring it up tomorrow during the experiment to record measurements and check your math in real time.

  1. Tonight (~20 min): Read the four Theory cards below. Then work through the Pre-lab Calculations — every Balmer line shows the full Rydberg-formula arithmetic so you can copy the work onto your paper sheet.
  2. Open this page on your phone tomorrow. Once it's loaded it works offline; everything you type saves automatically to that browser. No account, no sign-in, no shared data.
  3. In lab: work through Data Entry top-to-bottom. As you read each wavelength off the spectrometer scale, type it into the matching row. Photon energy auto-computes; the match pill turns ✓ green when you're within ±5 nm of the expected line.
  4. End of lab: fill in the two Conclusion sentences. Reveal the suggested wording if you want a model answer to compare to.
📐Reading the spectrometer scale. Hold the unit horizontally with the slit aimed at the lit source. Look through the eyepiece (the diffraction-grating side). The colored lines appear superimposed on a printed scale. The top scale (≈ 1.7 to 3.4) reads photon energy in eV. The bottom scale (≈ 700 down to 400) reads wavelength in nm. Wavelength is usually easier — use that, and the page will compute the energy for you.
🔄Don't see colors? Rotate the diffraction-grating eyepiece by 90°. The grating lines have a preferred orientation; turn it until the rainbow appears.
👥Sharing this page with a classmate? Each person's browser saves data independently — your measurements never leave your phone, and theirs never reach you. No interference between users.

1Theory Read first

A spectrometer separates light into its component wavelengths. You'll use it to compare a hot solid (continuous spectrum) with hot gases (line spectra). Tap each card to expand.

A · How a diffraction-grating spectrometer works

Your handheld spectrometer is a small box with three working parts:

  1. Slit — admits a narrow beam of source light.
  2. Diffraction grating — a clear plastic film with tens of thousands of parallel lines etched into it. Each line acts as a coherent secondary source.
  3. Wavelength/energy scale — printed inside the box; you read the position of each color line directly off it.

The waves from neighbouring grating lines interfere. Constructive interference occurs at angles where the path difference between adjacent lines equals a whole number of wavelengths:

$$ d \sin\theta = m\lambda $$
dline spacing of the grating (≈ 1/(grooves per mm))
θdiffraction angle from the central beam
morder of the maximum (m = ±1, ±2, …)
λwavelength of the light

Different wavelengths diffract at different angles, so the grating spreads white light into a rainbow. In your handheld unit the grating is the eyepiece, so the diffraction pattern actually forms on your retina, and your eye perceives it as bright lines on the printed scale.

OpenStax, College Physics 2e, §27.4 — Multiple Slit Diffraction.
B · Photon energy from wavelength

Light is quantized: each photon carries a discrete energy set by its frequency.

$$ E = hf = \frac{hc}{\lambda} $$

For numerical work in this lab, the convenient short form (with λ in nanometres):

$$ E\,(\text{eV}) = \frac{1240}{\lambda\,(\text{nm})} $$
Ephoton energy
hPlanck's constant = 6.626 × 10⁻³⁴ J·s
cspeed of light = 2.998 × 10⁸ m/s
ffrequency (Hz)
λwavelength
1240= hc in eV·nm — combines all the conversion factors
OpenStax, College Physics 2e, §29.1 — Quantization of Energy.
C · Continuous vs. line spectra

Hot solid → continuous (blackbody) spectrum. In a tungsten filament the atoms are locked into a lattice and electrons can take essentially any energy. They radiate at every wavelength inside a smooth envelope (Planck's curve), giving a full rainbow.

Hot low-pressure gas → discrete line spectrum. Free atoms have quantized electronic energy levels. An electron can only emit a photon whose energy exactly matches the gap between two allowed levels:

$$ E_{\text{photon}} = E_{n_2} - E_{n_1} $$

Because every element has its own unique pattern of energy levels, every element has a unique fingerprint of emission lines — the basis of all of spectroscopy.

OpenStax, College Physics 2e, §29.2 (photon model) and §30.3 (line spectra).
D · Bohr model & the Balmer series (the math for hydrogen)

Hydrogen is the simplest atom — one proton, one electron — and Niels Bohr's 1913 model gives its energy levels exactly:

$$ E_n = -\frac{13.6\,\text{eV}}{n^2} \qquad n = 1, 2, 3, \dots $$

When an electron drops from a higher level $n_2$ to a lower level $n_1$, a photon is emitted with energy $\Delta E = 13.6\,(\tfrac{1}{n_1^2} - \tfrac{1}{n_2^2})$ eV. The corresponding wavelength is given by the Rydberg formula:

$$ \frac{1}{\lambda} = R\left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right) $$
RRydberg constant = 1.0974 × 10⁷ m⁻¹ = 0.010974 nm⁻¹
n₁lower energy level (final state)
n₂upper energy level (initial state, n₂ > n₁)

The Balmer series is the special case $n_1 = 2$. Every transition that ends at level 2 produces a photon, and only these happen to fall in the visible part of the spectrum (the Lyman series at $n_1 = 1$ is UV; Paschen at $n_1 = 3$ is IR). The four Balmer lines you can actually see come from $n_2 = 3, 4, 5, 6$.

OpenStax, College Physics 2e, §30.3 — Bohr's Theory of the Hydrogen Atom.

2Pre-lab Calculations Do before lab

The lab worksheet (page 4) asks you to predict the visible hydrogen lines from theory. The table below does the Rydberg arithmetic for you so you can copy the answers onto your paper sheet.

Balmer-series predictor (n₁ = 2)

n₂
λ (nm)
E (eV)
Color
f (×10¹⁴ Hz)
Visible?

Wavelength from $1/\lambda = R(1/4 - 1/n_2^2)$ with $R = 0.010974\,\text{nm}^{-1}$. Energy from $E = 1240/\lambda$.

Worked example — calculating Line 1 by hand

The lab worksheet asks you to show your calculations for the four hydrogen lines. Here's the full arithmetic for Line 1; the other three lines (in the Q2 section below) follow exactly the same pattern with $n_2 = 4, 5, 6$.

👀 Step-by-step: Line 1 (n=3 → 2)

Step 1. Start with the Rydberg formula:

$$ \frac{1}{\lambda} = R\left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right) $$

Step 2. Substitute the constants. Balmer means $n_1 = 2$. For Line 1 the upper level is $n_2 = 3$. Use $R = 0.010974\,\text{nm}^{-1}$ so the answer comes out in nm directly:

$$ \frac{1}{\lambda} = 0.010974 \times \left(\frac{1}{2^2} - \frac{1}{3^2}\right) = 0.010974 \times \left(\frac{1}{4} - \frac{1}{9}\right) $$

Step 3. Find a common denominator inside the bracket:

$$ \frac{1}{4} - \frac{1}{9} = \frac{9}{36} - \frac{4}{36} = \frac{5}{36} \approx 0.13889 $$

Step 4. Multiply:

$$ \frac{1}{\lambda} = 0.010974 \times 0.13889 = 0.0015241\,\text{nm}^{-1} $$

Step 5. Invert to get the wavelength:

$$ \lambda = \frac{1}{0.0015241} \approx 656.1\,\text{nm}\;\;\checkmark $$

Step 6. Convert to photon energy with the shortcut $E\,(\text{eV}) = 1240/\lambda\,(\text{nm})$:

$$ E = \frac{1240}{656.1} \approx 1.89\,\text{eV}\;\;\checkmark $$

Check your color: 656 nm sits in the 625–750 nm red band — and the H-α line is famously the bright red one in any hydrogen spectrum. ✓

📚Why textbooks say 656.3 nm. The Rydberg formula gives the wavelength in vacuum. Air has a refractive index ≈ 1.0003, which shifts the observed wavelength by about 0.2 nm. So spectroscopy tables list H-α as 656.279 nm in air while the formula predicts 656.1 nm in vacuum. Both are correct — they're just measured under different conditions. Your handheld spectrometer can't resolve a 0.2 nm difference anyway.

Worksheet questions (page 4)

Q1 · How many lines do you expect to observe in the hydrogen emission spectrum?
Four visible lines (Balmer series, $n_2 = 3, 4, 5, 6 \rightarrow 2$). The series itself contains infinitely many transitions, but for $n_2 \geq 7$ the wavelengths drop below ≈ 397 nm and become UV — invisible to the human eye.
Q2 · Colors, wavelengths, and energies of the four visible lines:
Q3 · What is the name of this series?
The Balmer series — discovered empirically by Johann Balmer in 1885, later explained by Bohr's quantum model in 1913. By definition: any hydrogen emission whose lower state is $n_1 = 2$.
Q4a · For this series, how many emission lines are there?
Mathematically infinite — every $n_2 = 3, 4, 5, \dots$ contributes a line. As $n_2 \to \infty$ the lines crowd into the series limit at 364.6 nm. Only the first four ($n_2 = 3, 4, 5, 6$) are visible to your eye.
Q4b · Why do you only expect to see those four lines?
All higher transitions ($n_2 \geq 7$) emit photons with energy > 3.10 eV, corresponding to wavelengths < 397 nm — that's the near-ultraviolet, which the cornea and lens of your eye absorb before the light ever reaches your retina.
Q4c · Shortest wavelength of the series? Longest?
Shortest: the series limit at λ = 364.6 nm ($n_2 \to \infty$, in the UV).
Longest: the first line at λ = 656.3 nm ($n_2 = 3 \to 2$, deep red — also called H-α).
Q4d · Which can you actually observe — the shortest or the longest?
The longest. The 656.3 nm H-α line is unmistakably bright and red. The shortest wavelength of the full series (364.6 nm) is UV and blocked by your eye; even the shortest visible Balmer line (410.2 nm) is dim because your eye is least sensitive at the violet end.

3In-lab Data Entry Fill in lab

Type each measured wavelength as you read it off your spectrometer scale. Photon energy auto-computes ($E = 1240/\lambda$). Match indicators light up when your reading is within ±5 nm of the reference. Everything saves automatically — refresh-safe.

Visible spectrum reference

380440490565590625750 nm

3.1 · Incandescent bulb (continuous spectrum) — worksheet §3

Each color of a hot solid covers a broad range of wavelengths. Record the wavelength at the center of each color band.

📋What to do: Aim your spectrometer at the lit incandescent (regular tungsten) bulb. You'll see a smooth, gap-free rainbow. For each color row below, eyeball the visual center of that color band on the wavelength scale and type that number in. The energy column fills in automatically. The "Typical band" hint is a sanity check — your reading should fall inside that range.
Color
Center λ (nm)
Energy (eV)
Typical band (hint)

3.2 · Fluorescent bulb (mercury + phosphors) — worksheet §4

Bright discrete lines from mercury vapor inside the tube, plus a softer phosphor continuum. Compare to the four lines reported by J. Beale (bealecorner.org).

📋What to do: Aim at a classroom fluorescent or compact-fluorescent (CFL) bulb. Unlike the incandescent, you'll see distinct narrow bright lines, not a smooth rainbow. Type each line's wavelength into its color row. Four of the rows have Beale's published reference values pre-filled — when your reading lands within ±5 nm, the match pill turns green. The Orange / Yellow / Violet rows are blank for any extra lines you spot.
Color
Measured λ (nm)
Energy (eV)
Beale reference
Match?

3.3 · Hydrogen gas tube — worksheet §4 part 2

Look for the four visible Balmer lines. Hydrogen leaks out of glass tubes and contaminants leak in, so you'll see extra faint lines — focus on the four expected wavelengths.

📋What to do: Use the hydrogen gas tube on the fixed-stand spectrometer (don't unplug it). Look for the four lines in this order, brightest to faintest: a deep red (≈ 656), a cyan (≈ 486), a violet (≈ 434), and a faint deeper violet (≈ 410). Type each measured wavelength into its row; the page will show how close you are to the textbook value.
⚠️Heads up: The lab guide warns that gas tubes contaminate easily — chemicals leak in from the glass, oils from handling. You'll likely see extra faint lines that don't belong to hydrogen. Ignore them. Focus only on the four expected Balmer lines above.
Line
Measured λ (nm)
Energy (eV)
Expected λ (nm)
Match?

3.4 · Unknown gas tube #1 — worksheet §4 part 3

Pick any gas tube around the room. Record its brightest lines, then let the auto-matcher compare against the seven common gases (H, He, Ne, Hg, Ar, Kr, Na).

📋What to do: Pick a gas tube at random, but don't peek at the label first — the goal is to identify it from its spectrum. Record the brightest 3–6 lines you can see. As you type, the page identifies your color, finds the closest standard line in the database, and (below the table) ranks the seven candidate elements. You can also type your guess into the "Element name" field — the page tells you whether you guessed right.

Color
Measured λ (nm)
Energy (eV)
Closest standard (nm)
Best-match element

3.5 · Unknown gas tube #2

📋What to do: Same procedure as the first unknown — pick a different tube, record its brightest lines, see what the matcher reports. If the second tube turns out to be one of the same seven reference gases, the matcher will confirm; if it's something exotic (xenon, etc.) the matcher will say "no good match."

Color
Measured λ (nm)
Energy (eV)
Closest standard (nm)
Best-match element

4Conclusions Worksheet §6

Final two fill-in sentences. Type your own answers; reveal the suggested wording if you want to compare.

Q1 · Continuous spectrum was observed from while line spectra were observed from . Thus, we conclude that a hot solid will produce a spectrum and a hot gas will emit a spectrum.
Suggested wording
"Continuous spectrum was observed from the incandescent bulb, while line spectra were observed from the fluorescent bulb and the elemental gas tubes. Thus, a hot solid produces a continuous spectrum and a hot gas emits a line (discrete) spectrum."
Q2 · The spectra from different hot gases are . Describe its potential applications:
Suggested wording
"The spectra from different hot gases are unique to each element (a fingerprint). Applications: astronomical spectroscopy — identifying the chemical composition of stars and nebulae from their emission/absorption lines; forensic & remote chemical analysis — identifying gases in industrial leaks; plasma diagnostics — measuring temperature and density in fusion experiments; flame tests in chemistry; identification of neon-sign gases; medical & laser engineering — choosing the right gas for a HeNe or argon-ion laser."