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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_forwardthe 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_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
- Consta 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. Correct Part E By Thomson's time, it was known that excited atoms emit light waves of only certain frequencies. In his model, the frequency of emitted light is the same as the ocillation frequency of the electron or electrons in the atom. What would the radius of a Thomson-model atom have to be for it to produce red light of frequency 4.63x1014 Hz ? (see Appendix F from the textbook for data about the electron) Express your answer in meters. ? - 3 R= 3 • 10¯ m…arrow_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_forwardAn old model of a hydrogen atom has the charge +e of the proton uniformly distributed over a sphere of radius a0, with the electron of charge -e and mass m at its center. (a) What would then be the force on the electron if it were displaced from the center by a distance r # a0? (b) What would be the angular frequency of oscillation of the electron about the center of the atom once the electron was released?arrow_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_forwardEarly 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. By that time time, it was known that excited atoms emit light waves of only certain frequencies. In his model, the frequency of emitted light is the same as the oscillation frequency of the electron (s) problems in the atom. What radius (in millimeter) would a Thomson-model atom need for it to produce red light of frequency 4.57 x 1014 Hz? (Don't express your answer in scientific notation)arrow_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
- Fill in the blanks.arrow_forwardThe net charge of an object can be found be summing the individual charges. Since charge is quantized, all net charges are just an integer multiple of the elementary charge. q =n e where q is the net charge and n is an integer. For example, sodium can be a +1 ion and chlorine can be a -1 ion. What does this mean concerning their charge and structure?arrow_forwardTwo protons (p) and two electrons (e) are arranged on a circle of radius r = 4 [cm], with angles 0₁ = 20°, 0₂ = 30°, 03 = 20° and 04 = 60°, as shown in the figure. (qp = +1.6 x 10-1⁹ [C] and qe = -1.6 x 10-¹⁹ [C]). The figure is not to scale. a the circle. 04 Ēnet = ( 02 P Find Enet, the net electric field vector produced at the center of ])i + ( [ ]) Ĵ [N/C] b. Where on the circle should a fifth point charge qo be placed (give its angle relative the +x-axis) and what is its value (calculate qo) in order to have Enet (the net electric field at the center of the circle) equals zero (Type the detailed solution to this question in the below box, Show all your calculation steps by typing in the box). X Fiarrow_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