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Structure of Atom question

2003 · Shift 0 · Q59
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Structure of Atom question

2003 · Shift 0 · Q59

JEE MainChemistryStructure of AtomMCQ+4 / −1
The de Broglie wavelength of a tennis ball of mass 60 g moving with a velocity of 10 meters per second is approximately
  1. A
    10-31 meters
  2. B
    10-16 meters
  3. C
    10-25 meters
  4. D
    10-33 meters
View written solutionFree

Correct answer: D

  1. Use de Broglie relation

    The de Broglie wavelength is given by λ=hmv\lambda = \frac{h}{mv}λ=mvh​ where:

    • h=6.626×10−34 J sh = 6.626 \times 10^{-34}\,\text{J s}h=6.626×10−34J s
    • m=60 g=0.06 kgm = 60\,\text{g} = 0.06\,\text{kg}m=60g=0.06kg
    • v=10 m s−1v = 10\,\text{m s}^{-1}v=10m s−1

  2. Calculate momentum

    mv=0.06×10=0.6 kg m s−1mv = 0.06 \times 10 = 0.6\,\text{kg m s}^{-1}mv=0.06×10=0.6kg m s−1

  3. Calculate wavelength

    λ=6.626×10−340.6\lambda = \frac{6.626 \times 10^{-34}}{0.6}λ=0.66.626×10−34​

    λ≈1.104×10−33 m\lambda \approx 1.104 \times 10^{-33}\,\text{m}λ≈1.104×10−33m

  4. Approximate the order of magnitude

    λ≈10−33 m\lambda \approx 10^{-33}\,\text{m}λ≈10−33m

  5. Check options

    • A: 10−3110^{-31}10−31 m
    • B: 10−1610^{-16}10−16 m
    • C: 10−2510^{-25}10−25 m
    • D: 10−3310^{-33}10−33 m

    The closest match is Option D.

Final Answer: 10−33 m\boxed{10^{-33}\,\text{m}}10−33m​ So, the correct option is D.

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