De Broglie's wave round an orbit
"De Broglie's wave round an orbit" is a free, interactive Class 12 Physics simulation for NEET and JEE, built on the NCERT section "De Broglie's explanation" in Atoms. An electron wave wrapped round a circular orbit that closes on itself only when a whole number of wavelengths fits. NEET has asked about this idea 2 times in 10 years of papers. JEE Main asked 33 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
From the lesson De Broglie's explanation in Atoms. Change the values and watch what happens.
What it shows
NCERT §12.6
An electron wave wrapped round a circular orbit that closes on itself only when a whole number of wavelengths fits.
Controls
3 to try
- Sliderorbit radius 0.2–5 Å
- Sliderelectron speed (λ = h/mv)
- Togglesnap to Bohr radii
Try this
Make the wave close smoothly with exactly 3 wavelengths round the orbit and read mvr = 3h/2π.
In NEET
10 years of papers
Asked 2 times in 10 years of NEET.
See the past questions: Bohr's Atomic Model, Atoms (chapter)
In JEE Main
42 shifts analysed
33 questions from Atoms across the 42 JEE Main shifts Lumi has analysed (2017–2026).
The idea behind it
NCERT §12.6
- Bohr's second postulate, L = nh/2π, is the most puzzling one: why only whole multiples of h/2π? Louis de Broglie explained it in 1923, ten years after Bohr's model.
- De Broglie treated the orbiting electron as a particle wave (λ = h/p). Davisson and Germer confirmed the wave nature of electrons experimentally in 1927.
- On a plucked string only wavelengths with nodes at the ends survive, as standing waves; the others interfere with themselves on reflection and die away. In the same way, only an electron wave that fits the orbit exactly can persist.
- The condition is that the circumference holds a whole number of wavelengths: 2πrn = nλ, n = 1, 2, 3 … (Eq. 12.12). Fig. 12.8 shows four wavelengths fitted round the orbit (n = 4).
- For speeds much less than c, λ = h/mvn, so 2πrn = nh/mvn, which rearranges to mvnrn = nh/2π: exactly Bohr's quantum condition.
- So the quantised orbits and energy levels come from the wave nature of the electron: only resonant standing waves survive.
Questions
4 answers
- What does the "De Broglie's wave round an orbit" simulation show?
- An electron wave wrapped round a circular orbit that closes on itself only when a whole number of wavelengths fits.
- Has NEET asked about this idea?
- Yes. NEET has asked about this idea 2 times in 10 years of papers.
- Does JEE Main ask questions from Atoms?
- Yes. JEE Main asked 33 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
- Is this simulation free?
- Yes. It is free and runs in the browser on a phone or a laptop. It belongs to the lesson "De Broglie's explanation" in Atoms (Class 12 Physics).
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