Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
12th Edition
ISBN: 9781259587399
Author: Eugene Hecht
Publisher: McGraw-Hill Education
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Chapter 43, Problem 12SP
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To determine
To show: That the diameter of the hydrogen atom is
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What is the average radius of the orbit of an electron in the n=2 energy level of an oxygen atom (Z=8)? Express your answer in pico-meters.
A triply ionised beryllium atom (Be+++, Z = 4) has only one electron in orbit about the nucleus. If the electron decays from the n = 3 level to the first excited state (n = 2), calculate the wavelength of the photon emitted. give your answer in units of nm, rounded to one decimal place.
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Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
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- 7.4. Four measurements are made of the wavelength of light emitted by certain atom. The results, in nanometers, are: 525 20, 570 t 40. 503 ± 10, 491 + 8, Find the weighted average and its uncertainty. Is the last measurement worth in- cluding?arrow_forwardWhat is the orbital radius of the n = 3 excited state in the Bohr model of the hydrogen atom in nanometers? The ground-state radius of the hydrogen atom is 0.529 × 10-10 m. Please give your answer with 3 decimal places.arrow_forwardA hydrogen atom is in its ground state (n, = 1) when a photon impinges upon it. The atom absorbs the photon, which has precisely the energy required to raise the atom to the n, = 3 state. (a) What was the photon's energy (in eV)? 12.089 ev (b) Later, the atom returns to the ground state, emitting one or more photons in the process. Which of the following energies describes photons that might be emitted thus? (Select all that apply.) O 13.6 ev O 1.89 eV V 12.1 eV O 10.2 ev There are two ways a hydrogen atom in the n, = 3 state can end up in the ground state. In the first, all of the energy goes into one photon and the electron moves directly into the ground state. (What would be the energy of that photon?) In the other, the electron "descends" in two stages, each accompanied by the emission of a photon. (What would be the energies of those two photons?)arrow_forward
- Suppose that the uncertainty in position of an electron is equal to the radius of the n=1n=1 Bohr orbit, about 0.529×10−10m0.529×10−10m. A) Calculate the minimum uncertainty in the corresponding momentum component. Express your answer in kilogram meters per second. B) Compare this with the magnitude of the momentum of the electron in the n=1n=1 Bohr orbit. Compare this with the magnitude of the momentum of the electron in the Bohr orbit. a) This is greater than the magnitude of the momentum of the electron in the n=1n=1 Bohr orbit. b) This is the same as the magnitude of the momentum of the electron in the n=1n=1 Bohr orbit. c) This is less than the magnitude of the momentum of the electron in the n=1n=1 Bohr orbit.arrow_forwardA triply ionised beryllium atom (Be+++, Z = 4) has only one electron in orbit about the nucleus. If the electron decays from the n 7 level to the first excited state (n = 2), calculate the wavelength of the photon emitted. Please give your answer in units of nm, rounded to one decimal place. Answer:arrow_forwardA hydrogen atom emits a photon when its electron shifts from a higher energy level to a lower one. Suppose that one atom emits a photon whose wavelength equals 656 nm. If the energy levels are defined by the quantum number n (where n = 1, 2, 3, ), what were the initial and final values of n? ni=. ? nf=. ?arrow_forward
- A hydrogen atom in an n=2 state absorbs a photon.What wavelength photons might be emitted by the atom following absorption?For your answer: You should find 10 total possible wavelengths, with the shortest being ~100 nm and the largest being ~1900nm. You should enumerate all of them.arrow_forwardEx. 20: Find the value of energy of electron in eV in the third Bohr orbit of hydrogen atom. (Rydberg's constant (R) = 1.097 × 107 m¹, Planck's constant (h) = 6.63 × 10-34 J-s, velocity of light in air (c) = 3 × 108 m/s).arrow_forwardThe wave function of a hydrogen atom is in an excited state is: -1/2 W221 = ( m6°)"2 (r/9a) exp(-r/3ao) sin0 cose e“. (a) What is the most probable value of r in this state? How does it relate to the Bohr model prediction for the radius? (b) What is the magnitude of the orbital angular momentum in this state? How does it compare with the Bohr model prediction? (c) Find the orientation of the orbital angular momentum in this state. (d) What is the shortest wavelength photon that the atom can emit making an allowed transition? Identify the terminal state (in Whilm form) and justify why the transition is allowed,arrow_forward
- An electron is in the nth Bohr orbit of the hydrogen atom. (a) Show that the period of the electron is T = n3t0 and determine the numerical value of t0. (b) On average, an electron remains in the n = 2 orbit for approximately 10 ms before it jumps down to the n = 1 (ground-state) orbit. How many revolutions does the electron make in the excited state? (c) Define the period of one revolution as an electron year, analogous to an Earth year being the period of the Earth’s motion around the Sun. Explain whether we should think of the electron in the n = 2 orbit as “living for a long time.”arrow_forwardIf, in 1 1 = Ry - you set ni = 1 and take n2 greater than 1, you generate what is known as the Lyman %3D series. Find the wavelength of the first mem- ber of this series. The value of ħ is 1.05457 × 10¬34 J.s; the Rydberg constant for hydrogen is 1.09735 × 10’ m¬'; the Bohr radius is 5.29177 × 10¬1" m; and the ground state energy for hydrogen is 13.6057 eV. Answer in units of nm. Consider the next three members of this se- ries. The wavelengths of successive members of the Lyman series approach a common limit as n2 → ∞. What is this limit? Answer in units of nm.arrow_forwardA) Calculate the de Broglie wavelength of a neutron (mn = 1.67493×10-27 kg) moving at one six hundredth of the speed of light (c/600). Enter at least 4 significant figures. (I got the answer 949.4 pm but it is wrong, please help) B) Calculate the velocity of an electron (me = 9.10939×10-31 kg) having a de Broglie wavelength of 230.1 pm.arrow_forward
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