MHT CET · Physics · Dual Nature of Matter
The de-Broglie wavelength of an electron in the ground state of the hydrogen atom is
- A \(\pi r^{2}\)
- B \(2 \pi r\)
- C \(\pi r\)
- D \(\sqrt{2 \pi r}\)
Answer & Solution
Correct Answer
(B) \(2 \pi r\)
Step-by-step Solution
Detailed explanation
According to Bohr's theory
\(
\begin{aligned}
m v r &=\frac{n h}{2 \pi} \\
2 \pi r &=\frac{n h}{m v} \\
2 \pi r &=n \lambda
\end{aligned}
\)
For \(\quad n=1, \lambda=2 \pi r\)
\(
\begin{aligned}
m v r &=\frac{n h}{2 \pi} \\
2 \pi r &=\frac{n h}{m v} \\
2 \pi r &=n \lambda
\end{aligned}
\)
For \(\quad n=1, \lambda=2 \pi r\)
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