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If the radius of the first Bohr orbit is 2x, then the de Broglie wavelength of an electron in the 4th orbit is nearly:

Correct answer: A. 16πx

  • A. 16πx
  • B. 8πx
  • C. 4πx
  • D. 32πx

Explanation

The de Broglie wavelength in the nth orbit is given by λ = 2πr/n. The radius of the nth orbit is rₙ = r₁n². Given r₁=2x, the radius of the 4th orbit is r₄ = 2x.4² = 32x. The wavelength is then λ = 2π(32x)/4 = 16πx.

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