Calculate the de Broglie wavelength associated with a body of mass 1.5 kg moving with a velocity of 100m/s.
wavelength = h/mv
To calculate the de Broglie wavelength, we can use the de Broglie wavelength equation:
λ = h / p
Where:
- λ is the de Broglie wavelength
- h is the Planck's constant (6.626 x 10^-34 J·s)
- p is the momentum of the body.
To obtain the momentum, we can use the equation:
p = m * v
Where:
- p is the momentum
- m is the mass of the body
- v is the velocity of the body.
Let's calculate the momentum (p) first:
p = 1.5 kg * 100 m/s
p = 150 kg·m/s
Now, we can calculate the de Broglie wavelength (λ):
λ = h / p
λ = 6.626 x 10^-34 J·s / 150 kg·m/s
To simplify the equation, we can convert the units of h to kg·m²/s:
λ = 6.626 x 10^-34 kg·m²/s / 150 kg·m/s
Calculating this equation yields the de Broglie wavelength:
λ ≈ 4.417 x 10^-36 meters