Calculate the kinetic energy (in J) of a neutron with wavelength 85.3 pm.
E = hc/wavelength. h is Planck's constant of 6.64E-34 Js, c is speed of light = 3E8 m/s, wavelength is given. Convert wavelength to m. 85.3 pm = 85.3E-12 m. Post your work if you get stuck.
I got E = 2.33E-14 J, but that doesn't seem to be the right answer. I'm not really sure where to go from here, do I use Ekinetic = 1/2*mv^2? I'm not sure what the value for speed would be though.
To calculate the kinetic energy of a particle, we can use the equation:
Kinetic energy (KE) = 1/2 * mass * velocity²
We can determine the velocity of the neutron using its wavelength and the relationship between momentum and wavelength, given by the de Broglie equation:
wavelength = h / (mass * velocity)
where:
- wavelength is the given value of 85.3 pm
- h is the Planck's constant, which is approximately 6.626 × 10^-34 J·s
- mass is the mass of a neutron, which is approximately 1.675 × 10^-27 kg
- velocity is the unknown value we need to calculate
Rearranging the equation, we can solve for velocity:
velocity = h / (mass * wavelength)
Substituting the known values, we get:
velocity = (6.626 × 10^-34 J·s) / (1.675 × 10^-27 kg * 85.3 × 10^-12 m)
After calculating the velocity, we can substitute it into the kinetic energy equation to find the answer.