Question

If the kinetic energy of a free electron doubles, its de-Broglie wavelength changes by the factor:

• A. $\frac{1}{\sqrt{2}}$
• B. $\sqrt{2}$
• C. $\frac{1}{2}$
• D. 2

Hint:

Wavelength is inversely proportional to the square root of kinetic energy.

Answer 1

The Correct Option is A

Step 1: Concept
The relationship between wavelength and kinetic energy ($K$) is $\lambda = \frac{h}{\sqrt{2mK}}$.
Step 2: Analysis
This implies $\lambda \propto \frac{1}{\sqrt{K}}$. If $K$ becomes $2K$, the new wavelength $\lambda' = \frac{h}{\sqrt{2m(2K)}} = \frac{\lambda}{\sqrt{2}}$.
Step 3: Conclusion
The wavelength changes by a factor of $1/\sqrt{2}$.
Final Answer: (A)