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If the de Broglie wavelength of an electron is equal to 10 - 3 times the wavelength of a photon of frequency 6 × 10 14 Hz , then the speed of the electron is equal to (Speed of light = 3 × 10 8 m s - 1 , Planck's constant = 6.63 × 10 - 34 J s , Mass of electron = 9.1 × 10 - 31 kg )

Options

  1. A1.45 × 10 6   m   s - 1
  2. B1.1 × 10 6   m   s - 1
  3. C1.7 × 10 6   m   s - 1
  4. D1.8 × 10 6   m   s - 1

Correct answer

A. 1.45 × 10 6   m   s - 1

Step-by-step solution

λ e = 10 - 3 λ p f p = 6 × 10 14   Hz = C λ p λ p = 3 × 10 8 6 × 10 14 = 0.5 × 10 - 6   m λ e = 0.5 × 10 - 9 = h m e v e v e = 6.63 × 10 - 34 9.1 × 10 - 31 × 0.5 × 10 - 9 = 1.45 × 10 6   m   s - 1

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