Question

If the kinetic energy of a particle is increased to 16 times, the percentage change in the de Broglie wavelength of a particle is

• A. \(40 \%\)
• B. \(60 \%\)
• C. \(75 \%\)
• D. \(80 \%\)

Hint:

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

Answer 1

The Correct Option is C

Step 1: Ratio of wavelengths:
$\frac{\lambda'}{\lambda} = \sqrt{\frac{K}{K'}} = \frac14$.

Step 2: Percentage:
$\frac{\lambda - \lambda'}{\lambda} \times 100 = (1 - 0.25) \times 100 = 75\%$.

Final Answer:
The change is $75\%$, option (C). \[ \boxed{75\%} \]