According to the wave-particle duality of matter by de-Broglie, which of the following graph plot presents most appropriate relationship between wavelength of electron (λ) and momentum of electron (p)?

Solution

Chemistry ma’am · 3 steps

Write λ = h/p first, then check the axes on each graph before you look at the shape.

1. The relation. de Broglie says every moving particle has a wavelength set by its momentum. Planck's constant h is fixed, so λ and p are inversely proportional.

   λ = h/p ⇒ λ p = h = constant

2. Expected shapes. When the product of two quantities is constant, a graph of one against the other is a rectangular hyperbola. When λ is plotted against 1/p, the graph is a straight line through the origin with slope h.

   Option	Axes (y against x)	Shape drawn	Shape expected
   (a)	λ against 1/p	curve	straight line through origin
   (b)	p against λ	straight line	hyperbola
   (c)	λ against p	straight line	hyperbola
   (d)	λ against p	hyperbola	hyperbola

3. So. Only graph (d) matches: as momentum increases, the wavelength falls along a hyperbola. The answer is (d).

The idea to keep. If y ∝ 1/x, plotting y against x gives a hyperbola, but plotting y against 1/x gives a straight line through the origin. Always read the axis labels before you judge the shape.

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