**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...

See similar textbooks

Similar questions

3. a) Draw the missing nucleus (in the open circles) to complete the following nuclear reactions. b) Write the complete balanced nuclear equations using the mass number, atomic number, and element or ionizing radiation symbols for each species (reactants and products) in the equation. = proton O neutron O= ·O ·O- O O O + positron + beta particle + gamma photon
The naturally occurring radioactive isotope 232Th does not make good fission fuel, because it has an even number of neutrons; however, it can be bred into a suitable fuel (much as 238U is bred into 239P ). What are Z and N for 232Th ?
Determine the missing element 3516S----à -10e + ?
6.) please see picture
585 P Cr Fe Ga 75 Bise 81Kr Sr 98 Tc 49 13 I 58 Hg 201T1 81 Some Radioactive Isotopes Useful in Medical Imaging Mode of Decay Isotope Carbon-11 Fluorine-18 Phosphorus-32 Chromium-51 Iron-59 Gallium-67 Selenium-75 Krypton-81m Strontium-81 Technetium-99m Iodine-131 Mercury-197 Thallium-201 B+, T, Y B+, y В Submit Answer E.C., Y B. Y E.C., Y E.C., y B T 3. Y E.C.. Y E.C., Y Half-life protons neutrons 20.3 m 109 m 14.3 d 27.7 d 44.5 d 78.3 h 118 d 13.3 s 22.2 m 6.01 h 8.04 d 64.1 h 3.05 d Use in Medical Imaging Brain scan to trace glucose metabolism Brain scan to trace glucose metabolism Detect eye tumors [Review Topics] [References] Use the References to access important values if needed for this question. Diagnose albinism, image the spleen and gastrointestinal tract Bone marrow function, diagnose anemias Whole-body scan for tumors Pancreas scan Lung ventilation scan Scan for bone diseases, including cancer Brain, liver, kidney, bone scans; diagnosis of damaged heart muscle Diagnosis of…
It is believed that two carbon-12 nuclei can react in the core of a supergiant star to form sodium-23 and hydrogen-1. Calculate the energy released from this reaction for each mole of hydrogen formed. 2C+C ⇒ Na + H 11 Particle Mass (amu) C-12. 12.000000 Na-23 22.989767 H-1 1.007825 (1 kg = 6.022 x 1026 amu; NA = 6.022 x 1023 mol-1, C = 2.99792458 × 108 m/s)
239 142 Indicate the number of protons and neutrons in the following nuclei: (a) 94 -Ри, (b) Ba, (c) potassium-41. 56
Complete and balance the following nuclear equations by including the missing particle. ▼ Part H+B+3? Express your answer as a single isotope. [Ξ ΑΣΦ c+ Submit Part D A chemical reaction does not occur for this question. n I_Xe+? Express your answer as a single isotope. == ]ΑΣΦ Submit Part E 6 Previous Answers Request Answer A chemical reaction does not occur for this question. Submit 3 ["= |ΑΣΦ Request Answer 230Th º,e+? Express your answer as a single isotope. ? C Request Answer ? A chemical reaction does not occur for this question. ? P Pearson Review | Constants | Perio
7
2.
2. In each pair of isotopes, indicate which one you would expect to be radioactive. Support your answer: a) 42MO95 or 43TC2 d) soHg195 or s0Hg196
3. a) Alpha particles of the same initial speed are shot at the same intensity toward gold, silver, and aluminum foils of the same thickness. They are observed at a detector at a fixed scattering angle, 0 0°. What would the ratios of the number of alpha particles scattered by the gold and silver foils to the aluminum foil, Au NaAl Na Ag NaAl and respectively, be? (ZAu = 79, ZAg = 47, ZA1 = 13). b) Compare the number of a particles of fixed kinetic energy scattered through an angle of 10° (call this Na (10°)) with the number scattered through an angle of 20⁰ (Na (20°)) for Rutherford scattering by a thin gold foil of fixed thickness. Compute Na (10⁰) No (20°)* Rutherford's scattering model assumes that the alpha particles experience a Coulomb repulsion, F = KZe from the nucleus of the foil's atom. If, in a head-on collision the alpha particle has enough energy to get inside a uniformly charged KaZer nucleus of radius R, the force law would change to F and Rutherford's R³ " point-nucleus…