Matter Waves Of Macroscopic Objects
A cricket ball of mass 0.15 kg is bowled at a speed of 40 m/s toward a batsman, and a student calculates its de Broglie wavelength to test the matter-wave idea.
Select the correct option:
Solution
Approximately 1.1 × 10⁻³⁴ m
The de Broglie relation λ=mvh, given in NCERT, applies to all matter, including everyday objects. For the cricket ball, momentum is p=mv=0.15×40=6.0 kg·m/s. Substituting into the relation gives λ=6.06.63×10−34=1.1×10−34 m. This wavelength is fantastically smaller than any nucleus, which is precisely why the wave nature of macroscopic objects is utterly unobservable and everyday objects appear purely particle-like. The value 1.1×10−32 m is wrong because it misplaces the exponent by two orders during the division. The value 6.6×10−34 m is wrong because it uses Planck's constant without dividing by the momentum of 6.0 kg·m/s. The value 1.1×10−24 m is wrong because it is ten orders of magnitude too large, an arithmetic error in the exponent. As stated in NCERT Class 12, Chapter 11, matter waves are significant only for very light particles like electrons, since large masses give immeasurably tiny wavelengths. This result illustrates the correspondence principle: quantum wave effects become utterly negligible for large masses, so classical mechanics accurately describes everyday motion. The de Broglie wavelength becomes experimentally accessible only for extremely light particles such as electrons, neutrons, or atoms moving slowly. A magnitude check confirms that a wavelength around 10−34 m is vastly below any measurable scale, explaining why we never see a cricket ball diffract.
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About This Question
- Subject
- physics
- Chapter
- dual nature of matter and radiation
- Topic
- matter waves of macroscopic objects
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
Approximately 1.1 × 10⁻³⁴ m
The de Broglie relation λ=mvh, given in NCERT, applies to all matter, including everyday objects. For the cricket ball, momentum is p=mv=0.15×40=6.0 kg·m/s. Substituting into the relation gives λ=6.06.63×10−34=1.1×10−34 m. This wavelength is fantastically smaller than any nucleus, which is precisely why the wave nature of macroscopic objects is utterly unobservable and everyday objects appear purely particle-like. The value 1.1×10−32 m is wrong because it misplaces the exponent by two orders during the division. The value 6.6×10−34 m is wrong because it uses Planck's constant without dividing by the momentum of 6.0 kg·m/s. The value 1.1×10−24 m is wrong because it is ten orders of magnitude too large, an arithmetic error in the exponent. As stated in NCERT Class 12, Chapter 11, matter waves are significant only for very light particles like electrons, since large masses give immeasurably tiny wavelengths. This result illustrates the correspondence principle: quantum wave effects become utterly negligible for large masses, so classical mechanics accurately describes everyday motion. The de Broglie wavelength becomes experimentally accessible only for extremely light particles such as electrons, neutrons, or atoms moving slowly. A magnitude check confirms that a wavelength around 10−34 m is vastly below any measurable scale, explaining why we never see a cricket ball diffract.
This medium difficulty physics question is from the chapter dual nature of matter and radiation, covering the topic of matter waves of macroscopic objects. It appeared in the 2025 exam.
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