According to de Broglie’s hypothesis, moving particles of matter (such as electrons) show
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → dual (wave-particle) nature
Option (1) only particle nature — Incorrect. De Broglie’s hypothesis gives every moving particle a wavelength \( \lambda=h/p \), so the particle picture alone is incomplete.
Option (2) only wave nature — Incorrect. The particle still has mass and momentum \( p=mv \), which are particle attributes.
Option (3) dual (wave-particle) nature — Correct. De Broglie reasoned that if radiation shows dual aspects, so should matter. In \( \lambda=h/p \) the wavelength \( \lambda \) is a wave attribute and the momentum \( p \) a particle attribute, linked by Planck’s constant.
Option (4) neither wave nor particle nature — Incorrect. A moving electron has momentum (a particle property) and a de Broglie wavelength (a wave property), so it shows both.
NCERT (2026-27):
Wave Nature of Matter – “… De Broglie proposed that the wave length λ associated with a particle of momentum p is given as”
\( \displaystyle \lambda=\frac{h}{p}=\frac{h}{mv} \qquad (11.5) \)
“… Equation (11.5) is known as the de Broglie relation and the wavelength λ of the matter wave is called de Broglie wavelength. The dual aspect of matter is evident in the de Broglie relation. On the left hand side of Eq. (11.5), λ is the attribute of a wave while on the right hand side the momentum p is a typical attribute of a particle. Planck’s constant h relates the two attributes.”