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MHT CET · Physics · Dual Nature of Matter

The kinetic energy of an electron is tripled, then the de-Broglie wavelength associated with it, will change by a factor

  1. A \(\frac{1}{3}\)
  2. B \(3\)
  3. C \(\sqrt{3}\)
  4. D \(\frac{1}{\sqrt{3}}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\sqrt{3}\)

Step-by-step Solution

Detailed explanation

Relation between kinetic energy and momentum is as follows:
\(P=\frac{1}{\sqrt{2 m K}}\)
If kinetic energy is tripled, the new momentum is given by,
\(P^{\prime}=\frac{1}{\sqrt{2 m(3 K)}}=\frac{P}{\sqrt{3}}\)
de-Broglie wavelength of an electron is the following ratio: \(\lambda=\frac{h}{P}\)
Therefore, on tripling the kinetic energy the wavelength will change to: \(\lambda^{\prime}=\frac{h}{P^{\prime}}=\sqrt{3}\left(\frac{h}{P}\right)=\sqrt{3} \lambda\)