Question

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

• A. $1/3$
• B. $\sqrt{3}$
• C. $1/\sqrt{3}$
• D. 3

Hint:

Wavelength is inversely proportional to the square root of Kinetic Energy.

Answer 1

The Correct Option is C

Step 1: Relation
The de-Broglie wavelength $\lambda$ is related to kinetic energy $K$ by: $\lambda = \frac{h}{\sqrt{2mK}}$. This implies $\lambda \propto \frac{1}{\sqrt{K}}$.
Step 2: Substitution
If the new kinetic energy $K' = 3K$, then the new wavelength $\lambda' \propto \frac{1}{\sqrt{3K}}$.
Step 3: Ratio
$\frac{\lambda'}{\lambda} = \frac{\sqrt{K}}{\sqrt{3K}} = \frac{1}{\sqrt{3}}$.
Final Answer: (c)