**Title: Understanding Rutherford Scattering****Content:**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 \((^4\text{He})\) from gold-197 nuclei \((^{197}\text{Au})\).The energy of the incoming helium nucleus was \(7.25 \times 10^{-13} \, \text{J}\), and the masses of the helium and gold nuclei were \(6.68 \times 10^{-27} \, \text{kg}\) and \(3.29 \times 10^{-25} \, \text{kg}\), respectively (note that their mass ratio is 4 to 197). Assume that the helium nucleus travels in the \(+\text{x-direction}\) before the collision.**Problem Statement:**(a) If a helium nucleus scatters to an angle of 132° 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 \(+\text{x-axis}\)) of the gold nucleus.- **Diagram Explanation:** - The diagram shows an incoming helium nucleus moving towards a gold nucleus along a straight path. - The helium nucleus is depicted with a green arrow labeled \(\vec{v_i}\), indicating its initial velocity. - Upon collision, the helium nucleus scatters at an angle of 132° relative to its initial path. - The gold nucleus deflects at an angle of 120° from its initial position.- **Inputs Required:** - \( ^4\text{He } \text{speed:} \ \_\_\ \text{m/s} \) - \( ^{197}\text{Au } \text{velocity:} \ \_\_\ \text{m/s} \) - \( ^{197}\text{Au } \text{direction:} \ \_\_\ ^\circ \text{ counterclockwise from the } +\text{x-axis} \)(b) What is the final kinetic energy (in J) of the helium nucleus?- **Input Required:** - \_\_\ J**Note:** This analysis helps illustrate the principles of nuclear structure and the behavior of subatomic particles during elastic collisions

I am solving only first three parts of the question as per the guidelines.

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 (197Au). The energy of the incoming helium nucleus was 7.25 × 10-13 J, and the masses of the helium and gold nuclei were 6.68 x 10-27 kg and 3.29 x 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 132° 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. 120° He nucleus ý. Gold nucleus 4Нe speed m/s 197 Au velocity m/s 197 Au direction ° counterclockwise from the +x-axis (b) 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 (*He) from gold-197 nuclei (197Au). The energy of the incoming helium nucleus was 7.25 × 10-13 J, and the masses of the helium and gold nuclei were 6.68 x 10-27 kg and 3.29 x 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 132° 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. 120° He nucleus ý. Gold nucleus 4Нe speed m/s 197 Au velocity m/s 197 Au direction ° counterclockwise from the +x-axis (b) What is the final kinetic energy (in J) of the helium nucleus?

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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