Calculate the wavelengths:
-A muon (a sub particle with the mass of 1.884 X 10^-25g) traveling at 320.0 m/s
-an electron (me=9.10939 x 10^-28g) moving at 3.85 x 10^6 m/s
-An 83.0kg athlete running a "4 minute mile" (i.e. 400min/mile)
de Broglie wavelength = h/m*v
Substitute and solve.
Post your work if you get stuck.
To calculate the wavelengths of the given entities, we need to use the de Broglie wavelength equation:
λ = h / p
Where:
- λ is the wavelength (in meters)
- h is the Planck's constant, which is approximately 6.62607015 × 10^-34 J·s
- p is the momentum of the particle (in kg·m/s)
Let's calculate the wavelengths for each case:
1. Muon:
Mass (m) = 1.884 × 10^-25 g
Velocity (v) = 320.0 m/s
First, let's convert the mass to kg:
mass (m) = 1.884 × 10^-25 g = 1.884 × 10^-28 kg
Now, calculate the momentum (p) using the formula:
momentum (p) = mass (m) × velocity (v):
p = (1.884 × 10^-28 kg) × (320.0 m/s)
Now, we can calculate the wavelength (λ) using the de Broglie wavelength equation:
λ = (6.62607015 × 10^-34 J·s) / (p)
2. Electron:
Mass (m) = 9.10939 × 10^-28 g
Velocity (v) = 3.85 × 10^6 m/s
Again, let's convert the mass to kg:
mass (m) = 9.10939 × 10^-28 g = 9.10939 × 10^-31 kg
Calculate the momentum (p) using the formula:
p = (9.10939 × 10^-31 kg) × (3.85 × 10^6 m/s)
Now, we can calculate the wavelength (λ) using the de Broglie wavelength equation:
λ = (6.62607015 × 10^-34 J·s) / (p)
3. Athlete:
Mass (m) = 83.0 kg
Velocity (v) = (1 mile / 4 minutes) x (1 hour / 60 minutes) x (1000 m / 1 km)
Convert the velocity to m/s:
velocity (v) = (1 / 4) × (1 / 60) × (1000 m/1 km)
Calculate the momentum (p) using the formula:
p = (83.0 kg) × (velocity v)
Now, we can calculate the wavelength (λ) using the de Broglie wavelength equation:
λ = (6.62607015 × 10^-34 J·s) / (p)
Plug in the values and calculate the wavelengths for each case.