Answered: Ernest Rutherford (the first New…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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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 7.12 ✕ 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 119° 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.

⁴He 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?

______________ J

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