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KCET · Physics · Atomic Physics

The de-Broglie wavelength associated with electron of hydrogen atom in this ground state is

  1. A \(0.3 Å\)
  2. B \(3.3 Å\)
  3. C \(6.26 Å\)
  4. D \(10 Å\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(3.3 Å\)

Step-by-step Solution

Detailed explanation

The angular momentum of electron in an orbit of radius \(r\) is,
\(m v r=\frac{n h}{2 \pi}\)
So, momentum in ground state,
\(p=m v=\frac{h}{2 \pi r}...(i)\)
The de-Broglie wavelength associated with an electron is
\(\lambda=\frac{h}{m v}=\frac{h}{p}=2 \pi r\) [from Eq. (i)]
As we know, in ground state of hydrogen atom, \(r=0.53 Å\)
\(\Rightarrow \quad \lambda=2 \pi \times 0.53 Å=3.3 Å\)