Understanding the Undetectable de Broglie Wavelength of a Basketball
Question:
Explain why the de Broglie wavelength of a basketball (mass of 1 kg) is undetectable.
Answer:
The de Broglie wavelength of an object is defined as:
λ = h / p = h / (mv)
Where:
- λ = de Broglie wavelength
- h = Planck’s constant (≈ 6.63 × 10⁻³⁴ J·s)
- m = mass of the object (for a basketball, 1 kg)
- v = velocity of the object (assume 10 m/s)
Momentum, p = mv = 1 kg × 10 m/s = 10 kg·m/s
⇒ λ = (6.63 × 10⁻³⁴) / 10 = 6.63 × 10⁻³⁵ meters
⇒ λ = (6.63 × 10⁻³⁴) / 10 = 6.63 × 10⁻³⁵ meters
Why is this wavelength undetectable?
- The resulting wavelength (~10⁻³⁵ m) is extremely small—even smaller than the size of an atomic nucleus.
- Such a tiny wavelength is far beyond the resolving power of any existing measurement instrument.
- Macroscopic objects like basketballs interact constantly with their environments. This leads to quantum decoherence, suppressing any observable wave-like behavior.
Conclusion:
While all matter possesses a de Broglie wavelength, the wave-like properties are only noticeable in microscopic particles (like electrons), where the wavelengths are comparable to their size. For macroscopic objects, the wavelength is effectively zero for practical purposes, making it undetectable.
✅ Final Answer:
The de Broglie wavelength of a basketball is undetectable due to its large mass, resulting in an extremely small wavelength (~10⁻³⁵ m), which is far below the threshold of measurable quantum effects in the macroscopic world.