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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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- 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_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_forwardConsta 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_forward
- Find 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_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 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_forward
- 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. 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_forwardFill in the blanks.arrow_forward
- Solar 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 e x 1.6 × 10-19 C and using the combined average of your measured values of Q, determine the charge density of a cubic meter (m3) of solar wind sample as a function of Q.arrow_forwardAn carly model of the atom, proposed by Rutherford after his discovery of the atomic nucleus, had a positive point charge +Ze (the nucleus) at the center of a sphere of radius R with uniformly distributed negative charge -Ze. Z is the atomic number, the number of protons in the nucleus and the number of clectrons in the negative sphere. (a) Show that the clectric ficld inside this atom is Ze Ein = 1 r2 R3 (b) What is E at the surface of the atom? Is this the expected value? Explain. (c) A uranium atom has Z 92 and R = 0.10 nm. What is the clectric ficld strength %3D at r =arrow_forward350 / 746 110% 33. Four parallel plates are connected in a vacuum as in Figure 4. An electron, essentially at rest, drifts into the hole in plate X and is accelerated to the right. The vertical motion of the electron continues to be negli- gible. The electron passes through holes W and Y, then continues moving toward plate Z. Using the information given in the diagram, calculate (a) the speed of the electron at hole W (b) the distance from plate Z to the point at which the electron changes direction (c) the speed of the electron when it arrives back at plate X S a 37. I 38. f +4.0cm++4.0 cm+4.0 cm- t 3.0 x 102 V 5.0 x 10 V Figure 4 34. Two a particles, separated by an enormous distance, approach each other. Each has an initial speed ofarrow_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