Math Snap

STEP 1

Assumptions1. The speed of the electron is $.35 \times10^{6} \, \mathrm{m/s}$
. We will use the de Broglie formula to calculate the wavelength3. The mass of the electron is known and constant $9.11 \times10^{-31} \, \mathrm{kg}$
4. Planck's constant is known and constant $6.626 \times10^{-34} \, \mathrm{m^ kg / s}$

STEP 2

The de Broglie wavelength of a particle is given by the formula$$\lambda = \frac{h}{mv}$$where $\lambda$ is the wavelength, $h$ is Planck's constant, $m$ is the mass of the particle, and $v$ is the velocity of the particle.

STEP 3

Now, we plug in the given values for Planck's constant, the mass of the electron, and the velocity of the electron into the formula.
$$\lambda = \frac{6.626 \times10^{-34} \, \mathrm{m^2 kg / s}}{9.11 \times10^{-31} \, \mathrm{kg} \times2.35 \times10^{6} \, \mathrm{m/s}}$$

STEP 4

Perform the multiplication in the denominator.
$$\lambda = \frac{6.626 \times10^{-34} \, \mathrm{m^2 kg / s}}{2.14 \times10^{-24} \, \mathrm{kg \cdot m/s}}$$

Finally, divide the numerator by the denominator to find the wavelength.
$$\lambda = \frac{.626 \times10^{-34} \, \mathrm{m^2 kg / s}}{2.14 \times10^{-24} \, \mathrm{kg \cdot m/s}} =3.10 \times10^{-10} \, \mathrm{m}$$The de Broglie wavelength of an electron traveling with a speed of $2.35 \times10^{} \, \mathrm{m/s}$ is $3.10 \times10^{-10} \, \mathrm{m}$.