JEE Main · 2024 · Shift-ImediumATOM-071

According to the wave-particle duality of matter by de-Broglie, which of the following graph plots presents the most…

Structure of Atom · Class 11 · JEE Main Previous Year Question

Question

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

Options
  1. a

    image

  2. b

    image

  3. c

    image

  4. d

    image

Correct Answera

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Detailed Solution

🧠 The Inverse Pulse De Broglie's relationship (λ=h/p\lambda = h/p) is a classic inverse proportion. As momentum (pp) goes up, wavelength (λ\lambda) comes down.

🗺️ The Coordinate Logic

  1. The Equation: y1/xy \propto 1/x. In mathematics, this generates a rectangular hyperbola.
  2. Verification: Unlike a straight line, a hyperbola never touches the axes; it asymptotically approaches them. Momentum can be very large, but wavelength never hits true zero.

The y=1/xy = 1/x Identifier Whenever you see a product of variables equal a constant (pλ=hp\lambda = h), the graph in the first quadrant is always that characteristic "L-curve."

⚠️ Common Traps A linear downward slope is wrong! That would imply λ=abp\lambda = a - bp, which contradicts the theory.

Answer: (A)\boxed{\text{Answer: (A)}}

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