An atom of beryllium (m = 8.00 u) splits into two atomsof helium (m = 4.00 u) with the release of 92.2 keV ofenergy. Suppose the beryllium atom moved in the positive xdirection and had a kinetic energy of 44.0 keV. One of the heliumatoms is found to be moving in the positive x direction.Find the direction of motion of the second helium, and find thevelocity of each of the two helium atoms. Solve this problem in twodifferent ways: by direct application of conservation of momentumand energy; and by applying the results if the original berylliumatom is at rest to a frame of reference moving with the originalberyllium atom and then switching to the reference frame in whichthe beryllium is moving.
(a) by direct application of conservation of momentum andenergy
| velocity of the first helium(magnitude)Â Â Â Â | m/s |
| velocity of the second helium(magnitude)Â Â Â Â | m/s |
| direction of motion of the secondhelium    | |
(b) by applying the results if the original beryllium atom is atrest to a frame of reference moving with the original berylliumatom and then switching to the reference frame in which theberyllium is moving
| velocity of the first helium(magnitude)Â Â Â Â | m/s |
| velocity of the second helium(magnitude)Â Â Â Â | m/s |
| direction of motion of the second helium  |
