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A ball of mass 0.12 kg moving with a speed of 20 ms⁻¹ has de-Broglie wavelength ________. (h = 6.63 × 10⁻³⁴ Js)

Asked in GUJCET 2024 · de Broglie relation and its graphs

• (1) 2.76 × 10⁻³⁴ m
• (2) 1.76 × 10⁻³⁴ m
• (3) 3.76 × 10⁻³⁴ m
• (4) 4.76 × 10⁻³⁴ m

Step-by-step solution

Why the other options are wrong

• (2) No single slip produces 1.76×10⁻³⁴ m: that wavelength needs a momentum of 3.77 kg m s⁻¹, while the ball's is mv = 0.12×20 = 2.4 kg m s⁻¹. Sanity check: (6.63)/(2.4) = 2.76.
• (3) No single slip produces 3.76×10⁻³⁴ m: that wavelength belongs to a momentum of 1.76 kg m s⁻¹, not to the ball's 2.4 kg m s⁻¹.
• (4) No single slip produces 4.76×10⁻³⁴ m: it would need a momentum of 1.39 kg m s⁻¹, little more than half of mv = 2.4 kg m s⁻¹.

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