Photoelectrons, reduced mass and atomic excitation
| English | Español |
|---|---|
| work function/wɜːk ˈfʌŋkʃn/ | work function |
| reduced mass | reduced mass |
A decision before an answer
- Repeated equally spaced current dips can represent repeated losses of the same excitation energy, rather than a sequence of different atomic levels.
- Your goal: Distinguish photoelectric thresholds and characteristic X rays.
Read the relationship
- Photoelectric maximum kinetic energy is Kmax=hν−ϕ for photon frequency above threshold ν0=ϕ/h. A stopping-potential magnitude satisfies eVs=Kmax, so Vs is linear in ν above threshold. Increasing intensity at fixed frequency increases the available photon count and usually photocurrent, not maximum photoelectron energy. Below threshold the simple one-photon model emits no photoelectrons regardless of intensity. Work function is a property of the surface, not proportional to the illumination frequency.
- Apply reduced-mass spectral scaling and many-electron spin filling.
At fixed above-threshold frequency, increasing light intensity in the one-photon photoelectric model mainly changes:
More photons can emit more electrons; hν−ϕ remains the same.
Use the defining rule
- Characteristic X rays result when an electron fills an inner-shell vacancy, emitting a photon equal to the shell energy difference. Their sharp lines depend on target atoms. Bremsstrahlung arises from deceleration of energetic electrons in nuclear electric fields and produces a continuous background, with an energy endpoint set by the incident electron energy. A continuous background and discrete lines can appear together; the existence of one does not exclude the other. These mechanisms differ from visible fluorescence, phonon scattering and particle capture.
- Interpret Franck–Hertz energy spacing without inventing new levels.
For neutral oxygen ground configuration 1s²2s²2p⁴, Hund filling gives total electronic spin:
Three p orbitals fill singly first, then one pair; two unpaired parallel electrons give S=1.
Check the conditions
- For a hydrogen-like two-body atom, replace electron mass by reduced mass μ=m_eM/(m_e+M). In the simple Coulomb model, level energies scale as −μZ²/n², so spectral frequencies scale as μZ² and wavelengths inversely. For positronium M=m_e, μ=m_e/2 and its Rydberg constant is half the infinite-nuclear-mass value. For a heavy nucleus μ approaches m_e. In many-electron atoms, use orbital filling and Hund’s rule rather than the hydrogen model: degenerate orbitals are occupied singly with parallel spins before pairing. Carbon’s 2p² gives two unpaired electrons and total spin S=1; oxygen’s 2p⁴ has two unpaired electrons and also S=1. Filled pairs contribute zero net spin.
- Interpret Franck–Hertz energy spacing without inventing new levels.
Using h=4.136×10⁻¹⁵ eV·s, light at 8×10¹⁴ Hz has photon energy 3.3088 eV. With work function 2.0 eV, Kmax=1.3088 eV and stopping magnitude 1.3088 V. Excitation spacing 4 V gives 4 eV and, using hc≈1240 eV·nm, a 310 nm return photon. Positronium spectral wavelengths are twice the infinite-mass hydrogen values at matching transitions.
Positronium reduced mass divided by electron mass equals ____ (decimal).
m_e²/(2m_e)=m_e/2.
Apply the task format
- In Franck–Hertz experiments, accelerated electrons lose energy through inelastic excitation once they reach an atomic threshold. Repeated current-dip or peak spacing in accelerating voltage can therefore identify the same excitation energy lost one, two or more times. A spacing ΔV corresponds to energy eΔV; peaks at 4,8,12 V need not represent three separate excited-level energies. Contact potentials and retarding fields can shift absolute peak positions, so use the spacing and stated apparatus conditions. If the excited atom returns by one photon of that energy, wavelength is hc/(eΔV).
- Interpret Franck–Hertz energy spacing without inventing new levels.
Current intensity and stopping voltage answer different questions. Include reduced mass and orbital degeneracy, and use Franck–Hertz spacing rather than treating every peak as a new energy level.
Which answer fits this case?
Distinguish photoelectric thresholds and characteristic X rays
Equally spaced Franck–Hertz features necessarily identify a different atomic excitation energy at each successive feature.
Successive collisions can lose the same excitation energy repeatedly.
Keep the distinctions
- work function 逸出功 — Minimum energy required to remove an electron from the specified surface.
- reduced mass 约化质量 — Two-body effective mass m1m2/(m1+m2) for relative motion.
- Distinguish photoelectric thresholds and characteristic X rays.
- Apply reduced-mass spectral scaling and many-electron spin filling.
- Interpret Franck–Hertz energy spacing without inventing new levels.
Match each term with its precise meaning in this lesson.
Keep the distinctions stated in the teaching example.
Put this lesson’s reasoning or event sequence in order.
The order follows the stated process; check each stage before the next.