A body of mass, M, moving with velocity, V, has a wavelength, X, associated with it. This phenomenon is called----------

1. Analyze the question A moving body of mass M and velocity V is said to have a wavelength X. This is the idea that matter (particles) can behave like waves. We need the name of this phenomenon.

2. Explain the concept In 1924, Louis de Broglie proposed that every moving particle has a wave associated with it. Its wavelength is:

λ = h / (M V)

where h is Planck's constant (6.63 × 10⁻³⁴ J·s), M is the mass, and V is the velocity. This is called wave-particle duality (the "wave-particle paradox" in this question's wording), because matter shows both particle and wave properties.

3. Check each option

• A. Photoelectric effect: Electrons are ejected from a metal surface when light of sufficient frequency shines on it. It shows light behaving as particles (photons), not a wavelength for a moving mass.
• B. Heisenberg's uncertainty principle: We cannot know a particle's exact position and momentum at the same time. It is not about a wavelength associated with a moving body.
• C. Compton effect: X-rays scatter off electrons and lose energy, so their wavelength increases. It shows the particle nature of radiation.
• D. Wave-particle paradox: A moving particle has a wavelength associated with it (de Broglie relation). This matches the question.

4. Answer The correct option is D.

5. Tip When you see "mass, velocity and wavelength" together, think de Broglie, λ = h/mv, which means wave-particle duality. Link the other options to their keywords:

• photoelectric: electrons ejected by light
• Compton: X-ray scattering
• Heisenberg: position and momentum uncertainty