If λ and K are de Broglie wavelength and kinetic energy, respectively, of a particle with constant mass. The correct graphical representation for the particle will be :

Solution

Physics sir · 3 steps

Write λ in terms of K, then flip it round: 1/K turns out to be proportional to λ squared.

1. Momentum from K. For a particle of mass m, K = p²/2m, so p = √2mK. Put this into λ = h/p.

   λ = h/√2mK ⇒ 1/K = 2m/h² λ²

2. Read the shape. With m constant, 2m/h² is a fixed number, so 1/K ∝ λ². This is a parabola y = c x²: it starts at the origin, is flat there, and bends upward ever more steeply.
3. So. Only graph (d) starts flat at the origin and curves upward, so (d) is correct.

The idea to keep. For a material particle, λ ∝ 1/√K. Square both sides before you match a graph, and remember that y ∝ x² is an upward parabola through the origin.

Answer from the NTA final answer key. Solution by PrepWiser.