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CP Thomson’s Model of the Atom. Early in the 20th century, a leading model of the structure of the atom was that of English physicist J. J. Thomson (the discoverer of the electron). In Thomson’s model, an atom consisted of a sphere of positively charged material in which were embedded negatively charged electrons, like chocolate chips in a ball of cookie dough. Consider such an atom consisting of one electron with mass m and charge −e, which may be regarded as a point charge, and a uniformly charged sphere of charge +e and radius R. (a) Explain why the electron’s equilibrium position is at the center of the nucleus. (b) In Thomson’s model, it was assumed that the positive material provided little or no resistance to the electron’s motion. If the electron is displaced from equilibrium by a distance less than R, show that the resulting motion of the electron will be simple harmonic, and calculate the frequency of oscillation. (Hint: Review the definition of
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- In Thomson’s model, an atom is a positively charged spherical material in which negatively charged electrons are embedded like chocolate chips on a ball of cookie dough. Consider such an atom, made up of a uniformly charged sphere with charge +e and radius R and a point charge with mass m and charge −e. a. Locate the position of electrostatic equilibrium for the electron inside the sphere. b. Assume further that the sphere has little or no resistance to the electron’s mo- tion. If the electron is displaced from equilibrium by a distance less than R, show that the resulting motion of the electron would be simple harmonic. c. If the electron was displaced from equilibrium by a distance greater than R, would the electron oscillate? Would its motion be simple harmonic?arrow_forwardSolar wind is a flow of heavily charged ions emanating from the Sun’s corona. Spectroscopic analysis suggests it contains a density of approximately 5.0 electrons per cubic centimeter (cm3). Given that the elementary charge ? ≈ 1.6 × 10−19 ? and using the combined average of your measured values of Q 0.0375nC, determine the charge density of a cubic meter (m3) of solar wind sample as a function of Qarrow_forwardSuppose a capacitor consists of two coaxial thin cylindrical conductors. The inner cylinder of radius ra has a charge of +Q, while the outer cylinder of radius rh has charge -Q. The electric field E at a radial distance r from the central axis is given by the function: E = ae-r/ao + B/r + bo where alpha (a), beta (B), ao and bo are constants. Find an expression for its capacitance. First, let us derive the potential difference Vab between the two conductors. The potential difference is related to the electric field by: Vab = Edr = - Edr Calculating the antiderivative or indefinite integral, Vab = (-aager/ao + B + bo By definition, the capacitance Cis related to the charge and potential difference by: C = Evaluating with the upper and lower limits of integration for Vab, then simplifying: C = Q/( (e rb/ao - eTalao) + B In( ) + bo ( ))arrow_forward
- the situations (a) and (b). 13. Consider the following very rough model of a beryllium atom. The nucleus has four protons and four neutrons confined to a small volume of radius 10 -15 m. The two 1s electrons make a spherical charge cloud at an average -11 distance of 1-3x 10 m from the nucleus, whereas the two 2s electrons make another spherical cloud at an average distance of 5-2 x 10 the electric field at (a) a point just inside the 1s cloud and (b) a point just inside the 2s cloud. -11 m from the nucleus. Find 14. Find the magnitude of the electric fiold otarrow_forwardA Geiger counter is a device used to detect radiation, and consists of a thin metal wire (anode) at the center of a metallic tube (cathode). As radiation enters the tube, electrons are knocked off from the gas inside the tube or from the metallic wall, and accelerate towards the wire at the center. Consider a Geiger counter with an evacuated tube (a vacuum existing between cathode and anode), where the inner anode has a radius 2 mm and the outer cathode has a radius of 44 mm. The anode has a linear charge density of +10 nC/m, while the cathode has a charge per unit length of -10 nC/m. Let the cathode potential be equal to zero (using it as voltage reference). What is the potential at a distance of 73 mm from the center? Express your answer up to four significant figures. Note that this item is synced with the next item and that you can assume that the length of the Geiger counter is much larger than the radius of the cathode. Anode Cathodearrow_forwardFind the total charge contained in the 2 [cm] length of the cylindrical electron beam that is showed at the instant represented in the Figure, which is between z = 2 [cm] and z = 4 [cm], and has a radius of 1 [cm]. At that instant, the bulk density charge is assumed to be: p(r, z) = -5-10-6-e-10³rz X Zarrow_forward
- Suppose a capacitor consists of two coaxial thin cylindrical conductors. The inner cylinder of radius ra has a charge of +Q, while the outer cylinder of radius rh has charge -Q. The electric field E at a radial distancer from the central axis is given by the function: E = ae-r/ao + B/r + bo where alpha (a), beta (B), ao and bo are constants. Find an expression for its capacitance. First, let us derive the potential difference Vab between the two conductors. The potential difference is related to the electric field by: Vab = Edr = - Edr Calculating the antiderivative or indefinite integral, Vab = (-aaoe-r/ao + B + bo By definition, the capacitance C is related to the charge and potential difference by: C= Q I Vabarrow_forwardQuestion 1 a) In J. J. Thomson experiment (1897), an electron moving horizontally with a constant speed vo enters in between the horizontal plates of a capacitor. The electric field strength between the plates of length L and distance d, is E. The vertical deviation of the electron at the moment of exit from the field region is measured to be Y. Derive the expression giving the electron's charge to mass ratio, i.e. e/m to be 2v,Y/CEL). (Recall that Thomson received Nobel Prize for his achievement.) b) Calculate e/m, knowing the following data. E=1.6x10* Newton/Coulomb, L=10 cm, Y=2.9 cm, v=2.19x10* km/s. (Be careful to use coherent units.)arrow_forwardConstants In the early years of the 20th century, a leading model of the structure of the atom was that of the English physicist J. J. Thomson (the discoverer of the electron). In Thomson's model, an atom consisted of a sphere of positively charged material in which were embedded negatively charged electrons, like chocolate chips in a ball of cookie dough. Consider such an atom consisting of one electron with mass m and charge -e, which may be regarded as a point charge, and a uniformly charged sphere of charge +e and radius R. INU Submit Previous Answers v Correct Part B In Thomson's model, it was assumed that the positive material provided little or no resistance to the motion of the electron. If the electron is displaced from equilibrium by a distance r less than R. find the net force on the electron. Express your answer in terms of the variables R, e, vector r and constants a and en. Use the 'vec' button to denote vectors in your answers. ? F = Submit Previous Answers Request…arrow_forward
- Constants In the early years of the 20th century, a leading model of the structure of the atom was that of the English physicist J. J. Thomson (the discoverer of the electron). In Thomson's model, an atom consisted of a sphere of positively charged material in which were embedded negatively charged electrons, like chocolate chips in a ball of cookie dough. Consider such an atom consisting of one electron with mass m and charge -e, which may be regarded as a point charge, and a uniformly charged sphere of charge +e and radius R. Part A Is equilibrium position of the electron at the center of the nucleus. O Yes O No Submit Previous Answers v Correct Part B In Thomson's model, it was assumed that the positive material provided little or no resistance to the motion of the electron. If the electron is displaced from equilibrium by a distance r less than R, find the net force on the electron. Express your answer in terms of the variables R, e, vector r and constants T and en. Use the 'vec'…arrow_forwardConstants In the early years of the 20th century, a leading model of the structure of the atom was that of the English physicist J. J. Thomson (the discoverer of the electron). In Thomson's model, an atom consisted of a sphere of positively charged material in which were embedded negatively charged electrons, like chocolate chips in a ball of cookie dough. Consider such an atom consisting of one electron with mass m and charge -e, which may be regarded as a point charge, and a uniformly charged sphere of charge +e and radius R. O Yes O No Submit Previous Answers Correct Part B In Thomson's model, it was assumed that the positive material provided little or no resistance to the motion of the electron. If the electron is displaced from equilibrium by a distance r less than R, find the net force on the electron. Express your answer in terms of the variables R, e, vector r and constants T and en. Use the 'vec' button to denote vectors in your answers. Hνα ΑΣφ ? F = Submit Request Answerarrow_forwardA sample of HCl gas is placed in an electric field of 3×104NC−1. The dipole moment of each HCl molecule is 3.4×10−30Cm. Calculate the maximum torque experienced by each HCl molecule.arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning