AP EAMCET · PHYSICS · Dual Nature of Matter
. Hydrogen atom is in its \(n^{\text {th }}\) energy state. If de-Broglie wavelength of the electron is \(\lambda\), then
- A \(\lambda \propto \frac{1}{n^2}\)
- B \(\lambda \propto \frac{1}{n}\)
- C \(\lambda \propto n^2\)
- D \(\lambda \propto n\)
Answer & Solution
Correct Answer
(D) \(\lambda \propto n\)
Step-by-step Solution
Detailed explanation
Angular momentum of electron in \(n^{\text {th }}\) orbit of hydrogen is \[ L=m v r=\frac{n h}{2 \pi} \] de-Broglie wavelength, \(\lambda=\frac{h}{m v} \Rightarrow \frac{m v}{h}=\frac{1}{\lambda}\)…
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