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 7.35 x 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 112° 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.

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 7.35 x 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 112° 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.

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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Concept explainers

Relativistic Energy and Momentum

According to classical physics, time flow is the same for every observer. But according to einstein's theory, time flow is different for different observers. The idea that time flow is not the same for all may sound strange because we may not experience this effect in everyday life. This effect is only observed when an object moves with some velocity comparable to the velocity of light. This velocity is termed relativistic velocity.

Question

**Ernest Rutherford's Experiment with Helium and Gold Nuclei:**

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 \(7.35 \times 10^{-13}\) J, and the masses of the helium and gold nuclei were \(6.68 \times 10^{-27}\) kg and \(3.29 \times 10^{-25}\) 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 \(112^\circ\) 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.

- **\(^4\text{He}\) speed:** ____ m/s
- **\(^{197}\text{Au}\) velocity:** ____ m/s
- **\(^{197}\text{Au}\) direction:** ____ ° counterclockwise from the +x-axis

**(b)** What is the final kinetic energy (in J) of the helium nucleus?

- **Final kinetic energy:** ____ J

**Diagram Explanation:**
The diagram shows two nuclei before and after the collision:
- A helium nucleus (shown as a smaller cluster of particles) is moving towards the right with an initial velocity \(\vec{v}_i\).
- A gold nucleus (represented as a larger cluster) is shown scatter with the scattered angle marked as \(120^\circ\) from its initial path.
- After the collision, the helium nucleus is shown scattering at an angle of \(112^\circ\) relative to the +x axis.

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