Ernest Rutherford (the first New Zealander to be awarded the Nobel Prize in Chemistry) demonstrated that...

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Physics

Ernest Rutherford (the first New Zealander to be awarded theNobel Prize in Chemistry) demonstrated that nuclei were very smalland dense by scattering helium-4 nuclei (4He) from gold-197 nuclei(197Au). The energy of the incoming helium nucleus was 7.78 âœ• 10âˆ’13J, and the masses of the helium and gold nuclei were 6.68 âœ• 10âˆ’27kg and 3.29 âœ• 10âˆ’25 kg, respectively (note that their mass ratio is4 to 197). (Assume that the helium nucleus travels in the +xdirection before the collision.)
(a)
If a helium nucleus scatters to an angle of 130Â° during anelastic collision with a gold nucleus, calculate the heliumnucleus' final speed (in m/s) and the final velocity (magnitude inm/s and direction counterclockwise from the +x-axis) ofthe gold nucleus.
⁴He speed _____ m/s
¹⁹⁷Au velocity_ m/s
¹⁹⁷Au direction Â° counterclockwise from the+x-axis
(b)
What is the final kinetic energy (in J) of the heliumnucleus?
___ J

Answer & Explanation Solved by verified expert

4.1 Ratings (466 Votes)

aThe expression to find the kinetic energy isRearrange the expression for velocityHere is kinetic energy is mass and is initial velocity of HeliumSubstitute for and for in the expression of velocityAs collision is elastic apply conservation of momentum alongxaxisHere are the masses of helium and gold respectively See Answer

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