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Structure of Atom · JEE Preparation Chemistry

Calculate the wavelength (in nm) associated with a moving electron of mass 9.1 times 10^{-31} text{ kg} having a velocity of 3.0 times 10^6 text{ m s…

Practice question from Structure of Atom (JEE Preparation Chemistry), with the correct answer and a step-by-step solution.

medium · MCQ · Q-A4598F

Calculate the wavelength (in nm) associated with a moving electron of mass 9.1×10−31 kg9.1 \times 10^{-31} \text{ kg} having a velocity of 3.0×106 m s−13.0 \times 10^6 \text{ m s}^{-1}. (Planck's constant h=6.626×10−34 J sh = 6.626 \times 10^{-34} \text{ J s})

  1. A.2.42 nm
  2. B.0.242 nmCorrect answer
  3. C.24.2 nm
  4. D.0.024 nm

Solution

According to de Broglie's equation, λ=hmv=6.626×10−34(9.1×10−31)×(3.0×106)=2.42×10−10 m=0.242 nm\lambda = \frac{h}{mv} = \frac{6.626 \times 10^{-34}}{(9.1 \times 10^{-31}) \times (3.0 \times 10^6)} = 2.42 \times 10^{-10} \text{ m} = 0.242 \text{ nm}.

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