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In 1911, Ernest Rutherford and his assistants Geiger and Marsden
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Chapter 25 Solutions
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- A hydrogen atom when in its lowest energy state consists of a proton nucleus of charge +e (remember that +e = 1.6 x 10-19 C) and an electron of charge -e and mass of 9.1 x 10-31 kg. In the Bohr model of the atom, the electron moves around the nucleus in an approximately circular orbit with a radius of 0.52 x 10-10 m. The speed of the electron when in this lowest energy orbit is approximately 2.3 x 106 m/s. Imagine that we want to ionize this atom (that is free up the electron from its nucleus) by launching ANOTHER electron at the atom to break it apart. If we were to launch this electron from very far away from the atom, then how fast must it be launched in order to break apart the atom, so that all three particles (the proton and two electrons) end up at rest, very far apart?arrow_forwardAn atom of beryllium (m = 8.00 u) splits into two atoms of helium (m = 4.00 u) with the release of 92.2 keV of energy. If the original beryllium atom is at rest, find the kinetic energies and speeds of the two helium atoms.arrow_forwardA linear particle accelerator using beta particles collides electrons with their anti-matter counterparts, positrons. The accelerated electron hits the stationary positron with a velocity of 19 x 106 m/s, causing the two particles to annihilate.If two gamma photons are created as a result, calculate the energy of each of these two photons, giving your answer in MeV (mega electron volts), accurate to 1 decimal place. Take the mass of the electron to be 5.486 x 10-4 u, or 9.109 x 10-31 kg.Note: Assume that the kinetic energy is also converted into the gamma rays, and is included in the two photons.arrow_forward
- Consider an electron, of charge magnitude e = 1.602 × 10-1⁹ C and mass m₂ = 9.11 × 10-31 kg, moving in an electric field with an electric field magnitude E = 4 x 10² N/C, similar to what Thana observed in the simulation. Let the length of the plates be L = 50 cm, and the distance between them be d = 20 cm. Find the maximum speed, v, the electron could be moving if it enters the space halfway between and parallel to the two plates to just barely strike one of the plates. m/s If the field is pointing upward, which plate will Thana conclude the electron strikes at this speed? O The upper plate, because the electron charge magnitude is positive. O The upper plate, because we are only considering the magnitude of the electron charge, and magnitudes are always positive. O The lower plate, because the electron is attracted to the negative plate. O The lower plate, because the electron is negatively charged.arrow_forwardHelpful information: (1) An alpha particle is a helium nucleus, (2) e = 1.6 × 10-¹⁹ C, (3) k₂ = 9.0 × 10⁹ Nm² C-2, (4) 1nm = 1 × 10-⁹ m 1-An alpha particle lies on the x-axis, a distance of 1.0 nanometer from a proton (in this set-up, the alpha particle is at the origin while the proton is in the positive direction). Which of the following choices below represents the magnitude of the electric force on the alpha particle? (a) 2.3 × 10-10 N (b) 4.6 × 10-10 N (c) 2.3 x 10-19 N (d) 4.6 x 10-19 N cing the voltage so following insta choices below at a time! 1.00 s?arrow_forwardCalculate the speed (in m/s) of an electron and a proton with a kinetic energy of 1.15 electron volt (eV). (The electron and proton masses are me = 9.11 ✕ 10−31 kg and mp = 1.67 ✕ 10−27 kg. Boltzmann's constant is kB = 1.38 ✕ 10−23 J/K.) (a) an electron m/s (b) a proton m/s (c) Calculate the average translational kinetic energy in eV of a 3.09 ✕ 102 K ideal gas particle. (Recall from Topic 10 that 1 2 mv2 = 3 2 kBT.) eVarrow_forward
- The nucleus of an atom consists of protons and neutrons (no electrons). A nucleus of a carbon-12 isotope contains six protons and six neutrons, while a nitrogen-14 nucleus comprises seven protons and seven neutrons. A graduate student performs a nuclear physics experiment in which she bombards nitrogen-14 nuclei with very high speed carbon-12 nuclei emerging from a particle accelerator. As a result of each such collision, the two nuclei disintegrate completely, and a mix of different particles are emitted, including electrons, protons, antiprotons (with electric charge -e each), positrons (with charge +e each), and various neutral particles (including neutrons and neutrinos). For a particular collision, she detects the emitted products and find 17 protons, 4 antiprotons, 7 positrons, and 21 neutral particles. How many electrons are also emitted?arrow_forwardElectron capture is a variant on beta-radiation. The lightest nucleus to decay by electron capture is 7Be -- beryllium-7. The daughter nucleus is 7Li -- lithium-7. The electron is transformed into a massless particle (a neutrino): e − + 7 B e + ⟶ 7 L i + ν The initial electron is bound in the atom, so the beryllium mass includes the electron. In fact, since the electron starts bound in the atom, a more-accurate statement of the nuclear reaction is probably: 7 B e ⟶ 7 L i + ν The masses are beryllium: 7.016929 u, and lithium: 7.016003 u, and refer to the neutral atom as a whole. (Use uc and uc2 as your momentum and energy units -- but carry them along in your calculation.) The initial beryllium atom is stationary. Calculate the speed of the final lithium nucleus in km/s. (all the energy released goes into the lighter particle. c = 300,000 km/s)arrow_forwardElectron capture is a variant on beta-radiation. The lightest nucleus to decay by electron capture is 7Be -- beryllium-7. The daughter nucleus is 7Li -- lithium-7. The electron is transformed into a massless particle (a neutrino): e − + 7 B e + ⟶ 7 L i + ν The initial electron is bound in the atom, so the beryllium mass includes the electron. In fact, since the electron starts bound in the atom, a more-accurate statement of the nuclear reaction is probably: 7 B e ⟶ 7 L i + ν The masses are beryllium: 7.016929 u, and lithium: 7.016003 u, and refer to the neutral atom as a whole. (Use uc and uc2 as your momentum and energy units -- but carry them along in your calculation.) The initial beryllium atom is stationary. Calculate the speed of the final lithium nucleus in km/s. (You will make life much easier for yourself if you recognize that practically all the energy released goes into the lighter particle. c = 300,000 km/s)arrow_forward
- The mass of an electron is 9.11 x 10 ^-31 kg. The mass of a proton is 1.67 x 10 ^-27 kg. They are about 5.3×10^ −11 m apart in a hydrogen atom. What is the gravitational force between these two particles in the hydrogenatom?arrow_forwardSuppose a cyclotron is operated at an oscillator frequency of 12 MHz ( MegaHertz) and has a radius of R=53 cm. A deuteron, an isotope of hydrogen, consisting of a proton and a neutron and therefore having the same charge as a proton is to be accelerated in the cyclotron. Its mass, m=3.24 x10-27 kg. What is the resulting kinetic energy of the deuteron? Explain in not less than 3 sentences.arrow_forwardOne form of nuclear radiation, beta decay, occurs when a neutron changes into a proton, an electron and a neutral particle called a neutrino. When this change happens to a neutron within the nucleus of an atom, the proton remains behind in the nucleus while the electron and neutrino are ejected from the nucleus. The ejected electron is called a beta particle. One nucleus that exhibits beta decay is the isotope of hydrogen 3H, called tritium, whose nucleus consists of one proton (making it hydrogen) and two neutrons (giving tritium an atomic mass m = 3u). Tritium is radioactive, and it decays to helium. Suppose an electron is ejected from a 3H atom, which has a radius of 1.000×10-14 m. The resulting 3He atom has the same radius as the 3H atom. What is the escape velocity of the electron ejected from the process? Note: Your answer may be larger than the speed of light which is okay in this scenario. To solve this problem correctly we would need to use special relativity.arrow_forward
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