Why Are Electron Energies Limited?
Electron standing waves and the origin of allowed energy levels
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Why were electrons limited
Electron Standing Waves
School blocks YouTube? Use the file below. St. Mary's U. Astronomy and Physics Dept.
1. An electron is a standing wave. (A bound wave)
5 wavelengths
4 wavelengths
3 wavelengths
2 wavelengths
2. Circular standing waves can only be a whole number of wavelengths
Monterey Institute for Technology and Education
3. Limited wavelengths mean limited possible energies
Possible Electron Circumferences
= 2∏r = nλ
where n = 1,2,3,4 etc
Wavelength - describes probability of finding an electron at particular position.
Electron is a wave circled in on itself This standing wave has four cycles
The angular (circular) momentum of
...because a circular electron wave must be a whole number of wavelengths
Then C = 2(∏)r = nλ
where n = 1,2,3,4 etc
And λ = h/p = h/mv
Then … 2(∏)r = nh/mv
Angular Momentum = mvr = n[h/2∏]
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Check Your Understanding
5 quick questions — pick an answer to see if you’re right.
1. Why are electrons in atoms limited to certain energies?
2. An electron's orbit circumference is 2πr. Which condition must it satisfy?
3. An electron standing wave fits 4 wavelengths around its orbit. If λ = 1 × 10⁻¹⁰ m, what is the circumference?
4. An electron's angular momentum (mvr) is restricted to…
5. In this wave model, what does the electron's wave describe?
Why Is There a Maximum Electron Energy?
When light of a single frequency ejects electrons from a metal, the electrons come out with a range of kinetic energies, up to a sharp maximum. Increasing the brightness does not raise this maximum.
Which explanation best accounts for the sharp maximum?
▶ Want a challenge? Open 6 more Regents-style questions (harder · mixed formats)
Challenge score: 0 / 6
C1. Why do most electrons have less than the maximum kinetic energy?
C2. Light with a frequency of 1.2 × 1015 Hz shines on a metal with a work function of 2.3 eV. Substitute numerical values into a mathematical representation that can be used to determine the maximum kinetic energy of the ejected electrons. Then calculate it. (h = 4.14 × 10−15 eV·s)
C3. A photon with 4.0 eV of energy is absorbed by one of the least tightly bound electrons in a metal with a work function of 1.0 eV. Consider the electron–metal system, with the photon’s energy as the total energy, ET. Construct an energy bar graph for the system just after the electron escapes, where PE is the electric potential energy gained by separating the electron from the metal, and Eother is thermal energy (assume no collisions inside the metal).
Click a box to set each bar’s height; click it again to clear the bar to 0. The ET bar is drawn for you.
C4. A student makes the following claim.
Place a check mark in either the Support or Refute box. Justify your response using a mathematical relationship.
C5. Which quantity sets the maximum kinetic energy for a given metal?
C6. A student proposes that the maximum kinetic energy exists because electrons simply cannot move faster than a certain speed inside the metal. Describe evidence that contradicts this idea, and give an energy-based explanation for the maximum.