Question 20 of 62beginner🔧 ApplyNumerical2 marks

Calculate the wavelength of an electron moving with a velocity of 2.05×102.05 \times 10⁷ m s⁻¹.

Correct Answer

The wavelength of the electron is 3.55×10−113.55 \times 10^{-11} m (or 0.3550.355 Å).

Exercise: EXERCISES | Q: 2.20 | (Page 41)
For More Understanding

Explanation

To find the wavelength of a moving electron, we use the de Broglie equation, λ=hmv\lambda = \frac{h}{mv}, where hh is Planck's constant, mm is the mass of the electron, and vv is its velocity. Using the values provided in the context, we substitute h=6.626×10−34h = 6.626 \times 10^{-34} Js, m=9.1×10−31m = 9.1 \times 10^{-31} kg, and v=2.05×107v = 2.05 \times 10^7 m s−1^{-1} into the formula to calculate the wavelength.

Solution Steps

  1. Given values: Mass of electron, m=9.1×10−31m = 9.1 \times 10^{-31} kg Velocity of electron, v=2.05×107v = 2.05 \times 10^7 m s−1^{-1} Planck's constant, h=6.626×10−34h = 6.626 \times 10^{-34} Js

  2. Formula used: According to the de Broglie equation:

    λ=hmv\lambda = \frac{h}{mv}

  3. Substitute the values:

    λ=6.626×10−34 Js(9.1×10−31 kg)×(2.05×107 m s−1)\lambda = \frac{6.626 \times 10^{-34} \text{ Js}}{(9.1 \times 10^{-31} \text{ kg}) \times (2.05 \times 10^7 \text{ m s}^{-1})}

  4. Calculate the denominator: m×v=9.1×2.05×10−31+7=18.655×10−24m \times v = 9.1 \times 2.05 \times 10^{-31 + 7} = 18.655 \times 10^{-24} kg m s−1^{-1}

  5. Calculate the wavelength: λ=6.626×10−3418.655×10−24=0.3552×10−10\lambda = \frac{6.626 \times 10^{-34}}{18.655 \times 10^{-24}} = 0.3552 \times 10^{-10} m λ=3.55×10−11\lambda = 3.55 \times 10^{-11} m (or 0.3550.355 Å)

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