A)Calculate the wavelength of a 5.0kg bowling ball moving at 7.5m/s
b)an electro with a mass of 9.11 x 10^-13kg moving at 5.9 x 10^6 m/s.
To calculate the wavelength of an object, we need to use the de Broglie wavelength equation. The de Broglie wavelength (λ) is given by:
λ = h / p
Where:
λ = wavelength
h = Planck's constant (6.626 x 10^-34 J•s)
p = momentum of the object
Let's calculate the wavelength for each scenario:
a) For a 5.0 kg bowling ball moving at 7.5 m/s:
First, we need to calculate the momentum of the bowling ball using the formula:
p = m * v
Where:
m = mass of the bowling ball
v = velocity of the bowling ball
So, for the bowling ball:
p = 5.0 kg * 7.5 m/s = 37.5 kg•m/s
Now, we can calculate the wavelength (λ):
λ = h / p = (6.626 x 10^-34 J•s) / (37.5 kg•m/s) ≈ 1.767 x 10^-35 m
Therefore, the wavelength of the 5.0 kg bowling ball moving at 7.5 m/s is approximately 1.767 x 10^-35 meters.
b) For an electron with a mass of 9.11 x 10^-31 kg moving at 5.9 x 10^6 m/s:
First, we calculate the momentum of the electron:
p = m * v = (9.11 x 10^-31 kg) * (5.9 x 10^6 m/s) ≈ 5.371 x 10^-24 kg•m/s
Now, we can calculate the wavelength (λ):
λ = h / p = (6.626 x 10^-34 J•s) / (5.371 x 10^-24 kg•m/s) ≈ 1.234 x 10^-10 m
Therefore, the wavelength of the electron with a mass of 9.11 x 10^-31 kg moving at 5.9 x 10^6 m/s is approximately 1.234 x 10^-10 meters.