Calculate the wavelengths of the following objects. A muon (a subatomic particle with a mass of 1.884 imes $10-25 \mathrm{~g})$ traveling at $389 \mathrm{~m} / \mathrm{s}$ :

Question

Calculate the wavelengths of the following objects. A muon (a subatomic particle with a mass of 1.884 	imes $10-25 \mathrm{~g})$ traveling at $389 \mathrm{~m} / \mathrm{s}$ :

Accepted Answer

∻Solution∻ ‖ 1 ⋮ **Convert mass to kilograms**: The mass of the muon is given in grams and needs to be converted to kilograms for use in the de Broglie wavelength equation. The conversion is $1 ext{ kg} = 1000 ext{ g}$. Therefore, the mass of the muon in kilograms is $1.884 imes 10^{-25} ext{ g} imes \frac{1 ext{ kg}}{1000 ext{ g}} = 1.884 imes 10^{-28} ext{ kg}$. ‖ ‖ 2 ⋮ **Use the de Broglie wavelength equation**: The de Broglie wavelength $\lambda$ can be calculated using the equation $\lambda = \frac{h}{mv}$, where $h$ is Planck's constant ($6.626 imes 10^{-34} ext{ m}^2 ext{kg/s}$), $m$ is the mass of the particle in kilograms, and $v$ is the velocity of the particle in meters per second. ‖ ‖ 3 ⋮ **Calculate the wavelength**: Substitute the known values into the de Broglie equation to find the wavelength of the muon. $\lambda = \frac{6.626 imes 10^{-34} ext{ m}^2 ext{kg/s}}{1.884 imes 10^{-28} ext{ kg} imes 389 ext{ m/s}}$. ‖ ‖ 4 ⋮ **Perform the calculation**: After substituting the values, the calculation is $\lambda = \frac{6.626 imes 10^{-34}}{1.884 imes 10^{-28} imes 389} \approx 8.85 imes 10^{-13} ext{ m}$. ‖ ∻Answer∻ ⚹ The wavelength of the muon is approximately $8.85 imes 10^{-13}$ meters. ⚹ ∻Key Concept∻ ⚹ de Broglie wavelength ⚹ ∻Explanation∻ ⚹ The de Broglie wavelength is the wavelength associated with a particle and can be calculated using the particle's mass and velocity along with Planck's constant. ⚹◊What is the wavelength of the muon given its mass and velocity?⍭ Generate me a similar question◊

Sia