A steel ball of mass mis moving with a kinetic energy K. The de Broglie wavelength associated with the ball is

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AIIMS BSc NURSING 2023 Memory-Based Paper
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  1. \(\frac{\mathbf{h}}{2 \mathrm{mK}}\)
  2. \(\sqrt{\frac{\mathrm{h}}{2 \mathrm{mK}}}\)
  3. \(\frac{\mathrm{h}}{\sqrt{2 \mathrm{mK}}}\)
  4. meaningless

Answer (Detailed Solution Below)

Option 3 : \(\frac{\mathrm{h}}{\sqrt{2 \mathrm{mK}}}\)
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Detailed Solution

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Calculation:
The de Broglie wavelength λ is given by the formula:

λ = h / p

where:

  • h = Planck's constant
  • p = momentum of the particle

Since the steel ball is moving with kinetic energy K, the momentum p is related to K by the equation:

p = √(2mK)

Substitute this expression for p into the de Broglie wavelength equation:

λ = h / √(2mK)

The correct answer is: h / √(2mK)

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