Among the elementary subatomic particles of physics is the muon, which decays within a few nanoseconds after formation. The muon has a rest mass 1.126 109 times that of a proton. Calculate the de Broglie wavelength associated with a muon traveling at a velocity of 3.35 104 cm/s.
w = h/mv
h = Planck's constant
m = mass proton x factor in the problem in kg
v = velocity in m/s
1st I took 1.126e9 and multiplied it by 1.67262158e-27 kg to get your mass of 1.8833719e-18 kg. Then I did my dimensional analysis and had ((6.626e-34 J*s)*1s*100cm)/((1.8833719e-18 kg)(3.35e4 cm)*1m) and I got an answer of 1.05e-18 m using 3 sig figs. :)
To calculate the de Broglie wavelength associated with a particle, we can use the de Broglie wavelength formula:
λ = h / p
Where:
λ is the de Broglie wavelength
h is the Planck's constant (h = 6.62607015 x 10^-34 J*s)
p is the momentum of the particle
The momentum of a particle can be calculated using the formula:
p = mv
Where:
m is the mass of the particle
v is the velocity of the particle
Given:
Mass of a muon (m) = 1.126 x 10^9 times the mass of a proton = 1.126 x 10^9 * 1.67262192 x 10^-27 kg (mass of a proton)
Velocity of the muon (v) = 3.35 x 10^4 cm/s
First, we need to convert the velocity from cm/s to m/s:
v = 3.35 x 10^4 cm/s * (1 m / 100 cm)
v = 3.35 x 10^2 m/s
Now, we can calculate the mass of the muon in kilograms:
m = 1.126 x 10^9 * 1.67262192 x 10^-27 kg
m = 1.8829 x 10^-18 kg
Next, we can calculate the momentum of the muon:
p = m * v
p = (1.8829 x 10^-18 kg) * (3.35 x 10^2 m/s)
Now that we have the momentum, we can substitute it into the de Broglie wavelength formula:
λ = h / p
λ = (6.62607015 x 10^-34 J*s) / (1.8829 x 10^-18 kg * 3.35 x 10^2 m/s)
Calculating this expression will give us the de Broglie wavelength associated with the muon.