Answer to Question #145935 in General Chemistry for laisha

Question

What is the wavelength of an electron moving with a speed of 5.97 × 106 m/s? The mass of the electron is 9.11 × 10

Answer 1

Using the values of an electron's mass and velocity, the wavelength can be derived from the following equation:

$\lambda = \frac{h}{m\nu}$

where h is the Planck's constant and equals to $6.626 \times 10^{-34} J\cdot s$

To be consistent with the units:

$1J=1 \frac{kg\cdot m^2}{s^2}$

Thus the wavelength of the moving electron is:

$\lambda = \frac{h}{m\nu} = \frac{6.626\cdot 10^{-34} J \cdot s}{9.11 \cdot 10^{-31} kg \times 5.97\cdot10^6 m/s} \times \frac{1 \frac{kg\cdot m^2}{s^2}}{1 J} = \\=1.22 \cdot 10^{-10} m = 0.122 nm$