MHT CET · Physics · Dual Nature of Matter
The de-Broglie wavelength of an electron moving in the \(n^{\text {th }}\) Bohr orbit of radius \(r\) is
- A \(\frac{n r}{2 \pi}\)
- B \(\frac{2 \pi r}{n}\)
- C \(\frac{n r}{\pi}\)
- D \(n \pi r\)
Answer & Solution
Correct Answer
(B) \(\frac{2 \pi r}{n}\)
Step-by-step Solution
Detailed explanation
The de Broglie wavelength of an electron is given by
\(\lambda=\frac{h}{m v}\)
Taking the ratio of equation (1) and (2),
\(\frac{h}{\lambda}=\frac{n h}{2 \pi r}\)
\(\Rightarrow \lambda=\frac{2 \pi r}{n}\)
\(\lambda=\frac{h}{m v}\)
Taking the ratio of equation (1) and (2),
\(\frac{h}{\lambda}=\frac{n h}{2 \pi r}\)
\(\Rightarrow \lambda=\frac{2 \pi r}{n}\)
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