**Mass Spectrometry Analysis**A sample containing \( ^{12}\text{C} \), \( ^{16}\text{O} \), and an unknown isotope is analyzed in a mass spectrometer. As illustrated, the ions move in a semicircular path before hitting a photographic plate. The \( ^{12}\text{C}^+ \) and \( ^{16}\text{O}^+ \) ions are separated by 4.520 cm on the plate. The unknown isotope hits the plate 4.900 cm from the \( ^{12}\text{C}^+ \) ions. What is the mass of the unknown element?**Diagram Explanation:**- **Ion Source:** The ions start from an ion source and are initially at a low speed.- **Accelerating Potential (\(\Delta V\)):** The ions are accelerated through an electric potential difference, gaining kinetic energy. - **Uniform Magnetic Field (\( \mathbf{B} \)):** A uniform magnetic field is applied perpendicularly to the ion motion, causing the ions to move in a circular path.- **Path of Ions:** The ions follow a semicircular trajectory due to the perpendicular magnetic force.- **Photographic Plate or Detector:** The trajectory ends at a photographic plate that detects the ions and measures their separation.### CalculationUsing the radii differences and known masses, calculate the mass of the unknown isotope using the physics of circular motion and magnetic forces.

Radius of the circular path traced by a charge particle in the magnetic field is given by r=2Em12Bq…

Answered: A sample containing 12c, 160, and an…

Modern Physics

3rd Edition

ISBN:9781111794378

Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Publisher:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Chapter13: Nuclear Structure

Section: Chapter Questions

Problem 48P

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Rutherford fired a beam of alpha particles (helium nuclei) at a thin sheet of gold. An alpha particle was observed to be deflected by 90.0; its speed was unchanged. The alpha particles used in the experiment had an initial speed of 2 107 m/s and a mass of 6.7 1027 kg. Assume the alpha particle collided with a gold nucleus that was initially at rest. Find the speed of the nucleus after the collision.
When a nucleus (decays, does the (particle move continuously from inside the nucleus to outside? That is, does it travel each point along an imaginary line from inside to out? Explain.
Integrated Concepts Estimate the density of a nucleus by calculating the density of a proton, taking it to be a sphere 1.2 fm in diameter. Compare your result with the value estimated in this chapter.
If two nuclei are to fuse in a nuclear reaction, they must be moving fast enough so that the repulsive Coulomb force between them does not prevent them for getting within R1014mof one another. At this distance or nearer, the attractive nuclear force can overcome the Coulomb force, and the nuclei are able to fuse. (a) Find a simple formula that can be used to estimate the minimum kinetic energy the nuclei must have if they are to fuse. To keep the calculation simple, assume the two nuclei are identical and moving toward one another with the same speed v. (b) Use this minimum kinetic energy to estimate the minimum temperature a gas of the nuclei must have before a significant number of them will undergo fusion. Calculate this minimum temperature first for hydrogen and then for helium. (Hint: For fusion to occur, the minimum kinetic energy when the nuclei are far apart must be equal to the Coulomb potential energy when they are a distance R apart.)
Large amounts of depleted uranium (238U)are available as a by-product of uranium processing for reactor fuel and weapons. Uranium is very dense and makes good counter weights for aircraft. Suppose you have a 4000-kg block of 238U . (a) Find its activity, (b) How many calories per day are generated by thermalization of the decay energy? (c) Do you think you could detect this as heat? Explain.
(a) Calculate the energy released in the a decay of 238U. (b) What fraction of the mass at a single 238U is destroyed in the decay? The mass of 234Th is 234.043593 u. (c) Although the fractional mass loss is laws for a single nucleus, it is difficult to observe for an entire macroscopic sample of uranium. Why is this?
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Integrated Concepts Particles called muons exist in cosmic rays and can be created in particle accelerators. Muons are very similar to electrons, having the same charge and spin, but they have a mass 207 times greater. When muons are captured by an atom, they orbit just like an electron but with a smaller radius, since the mass in aB=h242mekqe2=0.5291010m is 207 me. (a)Calculate the radius of the n=1 orbit for a muon in a uranium ion (Z=92). (b) Compare this with the 7.5-fm radius of a uranium nucleus. Note that since the muon orbits inside the electron, it falls into a hydrogen-like orbit. Since your answer is less than the radius of the nucleus, you can see that the photons emitted as the muon falls into its lowest orbit can give information about the nucleus.
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