what is the wavelength of neutron (m=1.67x10^-27kg) travelling at 3.0x10^4 m/s?
To find the wavelength of a particle, such as a neutron, you can use the de Broglie wavelength equation. This equation relates the wavelength (λ) of a particle to its mass (m) and velocity (v) using Planck's constant (h).
The de Broglie wavelength equation is given by:
λ = h / (m * v)
Where:
λ = wavelength of the particle
h = Planck's constant (approximately 6.626 x 10^-34 J⋅s)
m = mass of the particle
v = velocity of the particle
Using the given values:
m = 1.67 x 10^-27 kg
v = 3.0 x 10^4 m/s
Let's plug these values into the equation to calculate the wavelength of the neutron.
First, substitute the values:
λ = (6.626 x 10^-34 J⋅s) / (1.67 x 10^-27 kg * 3.0 x 10^4 m/s)
Next, perform the multiplication and division:
λ = 2.51 x 10^-11 m
Therefore, the wavelength of the neutron with the given mass and velocity is approximately 2.51 x 10^-11 meters.