At what speed must a neutron travel to have a wavelength of 9.2 pm?
wavelength = h/mv
h = Planck's constant
m = mass in kg
v is velocity in m/s
So the solution to the problem is v= wavelength x h/m?
nope
is it V=h/m x wavelength
yes.
I put into my calculator (6.626e-34)/(9.109e-31)(0.92e-11)= 6.69e-15 m/s but it is wrong, so what did I mess up?
To determine the speed of a neutron needed to have a given wavelength, we can use the de Broglie wavelength equation:
λ = h / p
Where:
λ = wavelength
h = Planck's constant (6.62607015 x 10^-34 m^2 kg / s)
p = momentum
The momentum of a particle can be calculated using:
p = m * v
Where:
m = mass of the particle
v = speed of the particle
In this case, we are dealing with a neutron, which has a mass of approximately 1.67493 x 10^-27 kg.
First, we can rearrange the de Broglie wavelength equation to solve for momentum:
p = h / λ
Now, we can substitute the known values into the equation:
p = (6.62607015 x 10^-34 m^2 kg / s) / (9.2 x 10^-12 m)
To get the momentum, we divide the value of Planck's constant by the given wavelength:
p ≈ 7.19845 x 10^-23 kg m / s
Finally, we can substitute the momentum calculated into the momentum equation, solving for the speed:
7.19845 x 10^-23 kg m / s = (1.67493 x 10^-27 kg) * v
Solving for v:
v = (7.19845 x 10^-23 kg m / s) / (1.67493 x 10^-27 kg)
v ≈ 4.2936 x 10^4 m/s
Therefore, the neutron must travel at a speed of approximately 4.2936 x 10^4 m/s to have a wavelength of 9.2 pm.