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A body of mass 100 g moves at a speed of 36 km h⁻¹. The de Broglie wavelength associated with it is of the order of ______ m. (h = 6.626×10⁻³⁴ J s)

Asked in GUJCET 2014 · de Broglie relation and its graphs

• (1) 10⁻¹⁴
• (2) 10⁻²⁴
• (3) 10⁻³⁴
• (4) 10⁻⁴⁴

Step-by-step solution

Why the other options are wrong

• (1) No single slip gives 10⁻¹⁴ m (the size of a nucleus). Sanity check: p = 0.1×10 = 1 kg m s⁻¹, so λ = h/p is numerically equal to h: 6.6×10⁻³⁴ m.
• (2) No single slip gives 10⁻²⁴ m; it is ten powers of ten too large. With p = 1 kg m s⁻¹, λ = 6.6×10⁻³⁴ m.
• (4) No single slip gives 10⁻⁴⁴ m -- even leaving the mass in grams and the speed in km h⁻¹ only gives p = 3600 and λ ≈ 1.8×10⁻³⁷ m. The correct λ is 6.6×10⁻³⁴ m.

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