Velocity and kinetic energy of a neutron

[carus88]

Calculate the velocity and kinetic energy of a neutron (mass 1.675x10-27kg) that has a wavelength of 0.2nm. How does this compare to the average kinetic energy of a gas molecule at room temperature (0.038eV at 200C)?

1. E=mc^2

2. KE = 1/2 mv^2

I used 1. to calculate the energy which was 1.51 x10^-10 J

Then i subbed the energy into 2. and got a velocity of 4.24 x10^8 m/s

LOL obviously I'm going wrong some where how can a neutron be going faster than light!

CAN SOMEONE HELP PLEASE?

 

[Dick]

The energy you are computing is the rest energy, not the kinetic energy. To get the velocity use the de Broglie relation between wavelength and momentum. Then use that velocity to compute the kinetic energy.

 

[carus88]

sorry bout the multiple post i don't know how to delete the other one?

i used :

1. lambda=h/p=h/mv

an got v to = 1.98x10^3 m/s

then used ke = 0.5mv^2 = 0.0205eV

are these answers correct?

i attampted the the 2nd part and worked out a percentage
based on the respective energies an that the neutron had 46.1% less energy than the molecule

 

[Dick]

Looks right to me.

 

[carus88]

Thank you for your help.