Question

Identify the de-Broglie expression from the following

• A. \( \lambda = h \times p \)
• B. \( \lambda = h + p \)
• C. \( \lambda = h - p \)
• D. \( \lambda = \frac{h}{p} \)

Hint:

de-Broglie’s equation relates the wavelength of a particle to its momentum, emphasizing the wave-particle duality.

Answer 1

The Correct Option is D

Step 1: Understanding de-Broglie’s Hypothesis
Louis de-Broglie proposed that particles such as electrons could exhibit wave-like behavior.
He derived the equation for the de-Broglie wavelength \( \lambda \), which is given by: \[ \lambda = \frac{h}{p} \] Where:
\( \lambda \) is the de-Broglie wavelength,
\( h \) is Planck's constant,
\( p \) is the momentum of the particle.

Step 2: Explanation of Other Options
Option (b) is incorrect because it represents a sum of \( h \) and \( p \), which is not the correct de-Broglie expression.

Option (c) is incorrect because it represents a difference between \( h \) and \( p \), which is also incorrect.

Option (d) repeats option (a), which is correct.

Step 3: Conclusion Thus, the correct de-Broglie expression is \( \lambda = \frac{h}{p} \).