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What is the de-Broglie wavelength of a bullet of mass 0.033 kg travelling at the speed of 1 km/s? (h = 6.6 × 10⁻³⁴ Js)

Asked in GUJCET 2025 · de Broglie relation and its graphs

• (1) 3 × 10⁻²⁵ m
• (2) 2 × 10⁻³⁵ m
• (3) 1.1 × 10⁻³² m
• (4) 1.7 × 10⁻³⁵ m

Step-by-step solution

Why the other options are wrong

• (1) 3×10⁻²⁵ m is the textbook example's value for a dust particle (1.0×10⁻⁹ kg at 2.2 m s⁻¹), not for this bullet, whose momentum is 33 kg m s⁻¹.
• (3) 1.1×10⁻³² m is the textbook example's value for a 0.060 kg ball moving at 1 m s⁻¹, recalled instead of computed for this bullet.
• (4) 1.7×10⁻³⁵ m is the textbook example's value for a 0.040 kg bullet at 1 km s⁻¹ ((6.63×10⁻³⁴)/(40) ≈ 1.7×10⁻³⁵ m). This bullet is lighter, 0.033 kg, so its wavelength is the larger 2×10⁻³⁵ m.

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