What is the de Broglie wavelength of a proton that has a mass of 9.11 x 10^-31kg and travels a distance of 13km in 0.025 s? (h=6.63 x 10^-34 Js)
wavelength = h/mv
m is in kg.
You will need to change velocity from km/0.025s to m/s.
csaac
The answer is 1.57 x 10^2 m/s
oops jk wrong one^^^ it's actually 1.4 nm.... sorry
To find the de Broglie wavelength of a proton, we can use the equation:
λ = h / (m * v)
where λ is the de Broglie wavelength, h is the Planck's constant (6.63 x 10^-34 Js), m is the mass of the proton, and v is the velocity of the proton.
First, let's calculate the velocity of the proton. We can use the formula:
v = d / t
where v is the velocity, d is the distance traveled, and t is the time taken.
Given:
d = 13 km = 13,000 m (convert km to m)
t = 0.025 s
Plugging in the values:
v = (13,000 m) / (0.025 s)
v ≈ 520,000 m/s
Next, we substitute the known values into the equation for the de Broglie wavelength:
λ = (6.63 x 10^-34 Js) / ((9.11 x 10^-31 kg) * (520,000 m/s))
Calculating:
λ ≈ 1.274 x 10^-12 m
Therefore, the de Broglie wavelength of the proton is approximately 1.274 x 10^-12 meters.