Which of the following represent the variation of particle momentum a…

The correct answer is Option (3) → (A) only

The de Broglie relation is \( \lambda = h/p \), that is \( p\lambda = h \), a constant. So p is inversely proportional to \( \lambda \), and the graph of p against \( \lambda \) is a rectangular hyperbola: p very large for small \( \lambda \), falling steadily towards zero for large \( \lambda \).

(A) A curve falling steeply and then flattening out towards the \( \lambda \) axis — Correct. This is the hyperbola \( p = h/\lambda \).

(B) A straight line falling to zero at a finite \( \lambda \) — Incorrect. This would be \( p = a - b\lambda \), not a constant product.

(C) A curve rising with \( \lambda \) — Incorrect. p must fall as \( \lambda \) rises.

(D) A straight line through the origin — Incorrect. This is \( p\propto\lambda \), the opposite of the de Broglie relation.

(E) A horizontal line — Incorrect. This would mean p does not depend on \( \lambda \).

NCERT (2026-27):
Wave Nature of Matter – “… De Broglie proposed that the wave length \( \lambda \) associated with a particle of momentum p is given as

    \( \displaystyle \lambda = \frac{h}{p} = \frac{h}{mv} \qquad (11.5) \)

where m is the mass of the particle and v its speed. Equation (11.5) is known as the de Broglie relation and the wavelength \( \lambda \) of the matter wave is called de Broglie wavelength.”