De Broglie Wavelength
An electron in the first Bohr orbit of hydrogen has a de Broglie wavelength λ. What is the wavelength of the electron in the second orbit?
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About This Question
- Subject
- physics
- Chapter
- atoms and nuclei
- Topic
- de broglie wavelength
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
2λ
- Bohr's Postulate: For an orbit to be stable, its circumference must equal an integer multiple of the de Broglie wavelength:
- 2πrn=nλn.
- Radius Relation: Radius of nth orbit is rn=a0n2.
- Substitution:
- 2π(a0n2)=nλn
- λn=(2πa0)n
- Proportionality: λn∝n.
- Comparison:
- For n=1, λ1=λ.
- For n=2, λ2=2×λ1=2λ.
This medium difficulty physics question is from the chapter atoms and nuclei, covering the topic of de broglie wavelength. It appeared in the 2025 exam.
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