Velocity and kinetic energy of a neutron

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SUMMARY

The discussion focuses on calculating the velocity and kinetic energy of a neutron with a mass of 1.675 x 10-27 kg and a wavelength of 0.2 nm. Initially, the user incorrectly applied the mass-energy equivalence formula E=mc2 to compute energy as 1.51 x 10-10 J, leading to an unrealistic velocity of 4.24 x 108 m/s. Correcting the approach using the de Broglie wavelength formula, the user derived a velocity of 1.98 x 103 m/s and a kinetic energy of 0.0205 eV, concluding that the neutron has 46.1% less energy than a gas molecule at room temperature (0.038 eV at 200°C).

PREREQUISITES
  • Understanding of de Broglie wavelength and momentum relationship
  • Familiarity with kinetic energy calculations (KE = 1/2 mv2)
  • Basic knowledge of mass-energy equivalence (E=mc2)
  • Concept of energy comparison between particles at different states
NEXT STEPS
  • Study the de Broglie wavelength formula in detail
  • Learn about relativistic effects on particle velocities
  • Explore kinetic energy calculations for subatomic particles
  • Investigate the energy distribution of gas molecules at various temperatures
USEFUL FOR

Physics students, researchers in particle physics, and anyone interested in the behavior of subatomic particles and their energy dynamics.

carus88
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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?
 
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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.
 
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
 
Looks right to me.
 
Thank you for your help.
 

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