Ernest Rutherford (the first New Zealander to be awarded the Nobel Prize in Chemistry) demonstrated that nuclei were very small and dense by scattering helium-4 nuclei (4He) from gold-197 nuclei (197Au). The energy of the incoming helium nucleus was 7.52 ✕ 10−13 J, and the masses of the helium and gold nuclei were 6.68 ✕ 10−27 kg and 3.29 ✕ 10−25 kg, respectively (note that their mass ratio is 4 to 197). (Assume that the helium nucleus travels in the +x direction before the collision.) (a)If a helium nucleus scatters to an angle of 139° during an elastic collision with a gold nucleus, calculate the helium nucleus' final speed (in m/s) and the final velocity (magnitude in m/s and direction counterclockwise from the +x-axis) of the gold nucleus. What is the final kinetic energy (in J) of the helium nucleus?
Ernest Rutherford (the first New Zealander to be awarded the Nobel Prize in Chemistry) demonstrated that nuclei were very small and dense by scattering helium-4 nuclei (4He) from gold-197 nuclei (197Au). The energy of the incoming helium nucleus was 7.52 ✕ 10−13 J, and the masses of the helium and gold nuclei were 6.68 ✕ 10−27 kg and 3.29 ✕ 10−25 kg, respectively (note that their mass ratio is 4 to 197). (Assume that the helium nucleus travels in the +x direction before the collision.) (a)If a helium nucleus scatters to an angle of 139° during an elastic collision with a gold nucleus, calculate the helium nucleus' final speed (in m/s) and the final velocity (magnitude in m/s and direction counterclockwise from the +x-axis) of the gold nucleus. What is the final kinetic energy (in J) of the helium nucleus?
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Ernest Rutherford (the first New Zealander to be awarded the Nobel Prize in Chemistry) demonstrated that nuclei were very small and dense by scattering helium-4 nuclei (4He) from gold-197 nuclei (197Au). The energy of the incoming helium nucleus was 7.52 ✕ 10−13 J, and the masses of the helium and gold nuclei were 6.68 ✕ 10−27 kg and 3.29 ✕ 10−25 kg, respectively (note that their mass ratio is 4 to 197). (Assume that the helium nucleus travels in the +x direction before the collision.)
(a)If a helium nucleus scatters to an angle of 139° during an elastic collision with a gold nucleus, calculate the helium nucleus' final speed (in m/s) and the final velocity (magnitude in m/s and direction counterclockwise from the +x-axis) of the gold nucleus.
What is the final kinetic energy (in J) of the helium nucleus?
Transcribed Image Text:Ernest Rutherford (the first New Zealander to be awarded the Nobel Prize in Chemistry) demonstrated that nuclei were very small and dense by scattering helium-4
nuclei (“He) from gold-197 nuclei (19'Au). The energy of the incoming helium nucleus was 7.52 x 10-13 J, and the masses of the helium and gold nuclei were
-25
kg, respectively (note that their mass ratio is 4 to 197). (Assume that the helium nucleus travels in the +x direction before the
-27
6.68 x 10
kg and 3.29 × 10'
collision.)
(a) If a helium nucleus scatters to an angle of 139° during an elastic collision with a gold nucleus, calculate the helium nucleus' final speed (in m/s) and the final
velocity (magnitude in m/s and direction counterclockwise from the +x-axis) of the gold nucleus.
4Нe speed
m/s
197Au velocity
m/s
197Au direction
° counterclockwise from the +x-axis
(b) What is the final kinetic energy (in J) of the helium nucleus?
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