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NEET CHEMISTRYStructure of AtomEasy

Question

A 0.66 kg0.66 \text{ kg} ball is moving with a speed of 100 m/s100 \text{ m/s}. The associated wavelength will be: (h=6.6×10−34 Jsh = 6.6 \times 10^{-34} \text{ Js})

A

6.6×10−34 m6.6 \times 10^{-34} \text{ m}

B

1.0×10−35 m1.0 \times 10^{-35} \text{ m}

C

1.0×10−32 m1.0 \times 10^{-32} \text{ m}

D

6.6×10−32 m6.6 \times 10^{-32} \text{ m}

Step-by-Step Solution

According to the de Broglie equation, the wavelength (λ\lambda) associated with a material particle of mass mm moving with velocity vv is given by: λ=hmv\lambda = \frac{h}{mv}

Given: Mass, m=0.66 kgm = 0.66 \text{ kg} Velocity, v=100 m/sv = 100 \text{ m/s}

  • Planck's constant, h=6.6×10−34 Jsh = 6.6 \times 10^{-34} \text{ Js} (Note: The standard value is 6.626×10−346.626 \times 10^{-34}, but the question specifies 6.66.6).

Calculation: λ=6.6×10−34 kg m2s−10.66 kg×100 m s−1\lambda = \frac{6.6 \times 10^{-34} \text{ kg m}^2\text{s}^{-1}}{0.66 \text{ kg} \times 100 \text{ m s}^{-1}} λ=6.6×10−3466\lambda = \frac{6.6 \times 10^{-34}}{66} λ=0.1×10−34 m\lambda = 0.1 \times 10^{-34} \text{ m} λ=1.0×10−35 m\lambda = 1.0 \times 10^{-35} \text{ m}

This problem illustrates that for macroscopic objects (like a ball), the de Broglie wavelength is extremely small and not observable, consistent with the discussion in the NCERT text .

Exam Context & Concepts Covered

This question aligns with the NEET CHEMISTRY syllabus, specifically targeting concepts from Structure of Atom. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

CHEMISTRYStructure of Atommovingassociatedwavelength

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