College Physics
OER 2016 Edition
ISBN: 9781947172173
Author: OpenStax
Publisher: OpenStax College
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Chapter 30, Problem 14TP
To determine
The particle more likely found at a larger distance from the coordinate
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Consider a particle with mass m in an infinite square well of width L = 1, with energy E
(a) What energy state n is this particle in?
(b) What is the probability that the particle is in the range
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b.Draw the probability distribution for a particle in a box at the n-3 energy level.
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What is the wavelength of radiation emitted when it decays from the n-3 level to the n-
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A particle is confined in a box of length L.
The momentum is quantized and we find that the lowest possible value of the momentum for a particle in that box is 1.3 E-24 kg.m2/s.
What is the length of the box? Express your answer in Angstroms (1E-10 m)
Chapter 30 Solutions
College Physics
Ch. 30 - Name three different types of evidence for the...Ch. 30 - Explain why patterns observed in the periodic...Ch. 30 - If atoms exist, why can't we see them with visible...Ch. 30 - What two pieces of evidence allowed the first...Ch. 30 - How do the allowed orbits for electrons in atoms...Ch. 30 - How do the allowed orbits for electrons in atoms...Ch. 30 - Explain how Bohr's rule for the quantization of...Ch. 30 - What is a hydrogen-like atom, and how are the...Ch. 30 - Explain why characteristic x rays are the most...Ch. 30 - Why does the energy of characteristic x rays...
Ch. 30 - Observers at a safe distance from atmospheric test...Ch. 30 - Lasers are used to burn and read CDs. Explain why...Ch. 30 - Crystal lattices can be examined with x rays but...Ch. 30 - CT scanners do not detect details smaller than...Ch. 30 - How do the allowed orbits for electrons in atoms...Ch. 30 - Atomic and molecular spectra are discrete. What...Ch. 30 - Hydrogen gas can only absorb EM radiation that has...Ch. 30 - Lasers are used to burn and read CDs. Explain why...Ch. 30 - The coating on the inside of fluorescent light...Ch. 30 - What is the difference between fluorescence and...Ch. 30 - How can you tell that a hologram is a true...Ch. 30 - How is the de Broglie wavelength of electrons...Ch. 30 - What is the Zeeman effect, and what type of...Ch. 30 - Define the quantum numbers n,l,ml,s, and ms.Ch. 30 - For a given value of n, what are the allowed...Ch. 30 - For a given value of l, what are the allowed...Ch. 30 - List all the possible values of s and msfor an...Ch. 30 - Identify the shell, subshell, and number of...Ch. 30 - Which of the following are not allowed? State...Ch. 30 - Using the given charge-to-mass ratios for...Ch. 30 - (a) Calculate the mass of a proton using the...Ch. 30 - If someone wanted to build a scale model of the...Ch. 30 - Rutherford found the size of the nucleus to be...Ch. 30 - In Millikan's oil-drop experiment, one looks at a...Ch. 30 - (a) An aspiring physicist wants to build a scale...Ch. 30 - By calculating its wavelength, show that the first...Ch. 30 - Find the wavelength of the third line in the Lyman...Ch. 30 - Look up the values of the quantities in...Ch. 30 - Verify that the ground state energy E0 is 13.6 eV...Ch. 30 - If a hydrogen atom has its electron in the n=4...Ch. 30 - A hydrogen atom in an excited state can be ionized...Ch. 30 - Find the radius of a hydrogen atom in the n=2...Ch. 30 - Show that (13.6eV)/hc=1.097107m=R (Rydberg's...Ch. 30 - What is the smallest-wavelength line in the Balmer...Ch. 30 - Show that the entire Paschen series is in the...Ch. 30 - Do the Balmer and Lyman series overlap? To answer...Ch. 30 - (a) Which line in the Balmer series is the first...Ch. 30 - A wavelength of 4.653 m is observed in a hydrogen...Ch. 30 - A singly ionized helium ion has only one electron...Ch. 30 - A beryllium ion with a single electron (denoted...Ch. 30 - Atoms can be ionized by thermal collisions, such...Ch. 30 - Verify Equations rn=n2ZaB and...Ch. 30 - The wavelength of the four Balmer series lines for...Ch. 30 - (a) What is the shortest-wavelength x-ray...Ch. 30 - A color television tube also generates some x rays...Ch. 30 - An x ray tube has an applied voltage of 100 kV....Ch. 30 - The maximum characteristic x-ray photon energy...Ch. 30 - What are the approximate energies of the K and K...Ch. 30 - Figure 30.39 shows the energy-level diagram for...Ch. 30 - A helium-neon laser is pumped by electric...Ch. 30 - Ruby lasers have chromium atoms doped in an...Ch. 30 - (a) What energy photons can pump chromium atoms in...Ch. 30 - Some of the most powerful lasers are based on the...Ch. 30 - If an atom has an electron in the n=5 state with...Ch. 30 - An atom has an electron with m1=2. What is the...Ch. 30 - What are the possible values of m1 for an electron...Ch. 30 - What, if any, constraints does a value of ml=1...Ch. 30 - (a) Calculate the magnitude of the angular...Ch. 30 - (a) What is the magnitude of the angular momentum...Ch. 30 - Repeat Exercise 30.40 for l=3.Ch. 30 - (a) How many angles can L make with the z-axis for...Ch. 30 - What angles can the spin S of an electron make...Ch. 30 - (a) How many electrons can be in the n=4 shell?...Ch. 30 - (a) What is the minimum value of 1 for a subshell...Ch. 30 - (a) If one subshell of an atom has 9 electrons in...Ch. 30 - (a) List all possible sets of quantum numbers...Ch. 30 - Which of the following spectroscopic notations are...Ch. 30 - Which of the following spectroscopic notations are...Ch. 30 - (a) Using the Pauli exclusion principle and the...Ch. 30 - Integrated Concepts Estimate the density of a...Ch. 30 - Integrated Concepts The electric and magnetic...Ch. 30 - (a) What is the distance between the slits of a...Ch. 30 - Integrated Concepts A galaxy moving away from the...Ch. 30 - Integrated Concepts Calculate the velocity of a...Ch. 30 - Integrated Concepts In a Millikan oil-drop...Ch. 30 - Integrated Concepts What double-slit separation...Ch. 30 - Integrated Concepts In a laboratory experiment...Ch. 30 - Integrated Concepts Find the value of l, the...Ch. 30 - Integrated Concepts Particles called muons exist...Ch. 30 - Integrated Concepts Calculate the minimum amount...Ch. 30 - Integrated Concepts A carbon dioxide laser used in...Ch. 30 - Integrated Concepts Suppose an MRI scanner uses...Ch. 30 - Integrated Concepts (a) An excimer laser used for...Ch. 30 - Integrated Concepts A neighboring galaxy rotates...Ch. 30 - Integrated Concepts A pulsar is a rapidly spinning...Ch. 30 - Integrated Concepts Prove that the velocity of...Ch. 30 - Unreasonable Results (a) What voltage must be...Ch. 30 - Unreasonable Results A student in a physics...Ch. 30 - Construct Your Own Problem The solar corona is so...Ch. 30 - Construct Your Own Problem Consider the...Ch. 30 - Prob. 1TPCh. 30 - Prob. 2TPCh. 30 - Prob. 3TPCh. 30 - Prob. 4TPCh. 30 - Prob. 5TPCh. 30 - Prob. 6TPCh. 30 - Prob. 7TPCh. 30 - Prob. 8TPCh. 30 - Prob. 9TPCh. 30 - Prob. 10TPCh. 30 - Prob. 11TPCh. 30 - Prob. 12TPCh. 30 - Prob. 13TPCh. 30 - Prob. 14TPCh. 30 - Prob. 15TPCh. 30 - Prob. 16TP
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- It can be shown that the allowed energies of a particle of mass m in a two-dimensional square box of sided L are Enl =h2/8mL2 (n2 + l2)The energy depends on two quantum numbers, n and l, both of which must have an integer value 1, 2, 3,........a. What is the minimum energy for a particle in a twodimensional square box of side L?b. What are the five lowest allowed energies? Give your values as multiples of Emin .arrow_forwardWhat is the probability of finding a particle in the last 10% of a one-dimensional box for n = 1 state? Find the solution(s) to the differential equations: a. y''(x) + y'(x) - 6y(x) = 0 and b. y''(x) - 4y'(x) + 4y(x) = 0.arrow_forwardFor the particle in the box in the base state, calculate the quantities <x> and <Px> :arrow_forward
- Is the function, ψ(x) = A exp(-|x|), qualifies to be a wave function of a particle that can move along the entire real axis? Explain.arrow_forwarda. For the allowed energies of a particle in a box to be large, should the box be very big or very small? Explain.b. Which is likely to have larger values for the allowed energies: an atom in a molecule, an electron in an atom, or a proton in a nucleus? Explain.arrow_forwardA particle is in a box of length L. Suddenly, the length of the box is increased to 2L. What happens to the energy levels as shown? (a) nothing; they are unaffected. (b) They move farther apart. (c) They move closer together.arrow_forward
- A particle is created in a shower of particle decays. Its velocity is measured to a precision of 50 micrometers/second and its mass is inferred to be (exactly) 6.64×10−27 kg. What is the minimum uncertainty in our knowledge of the particle’s position? Explain.arrow_forwardChapter 39, Problem 025 The two-dimensional, infinite corral of the figure is square, with edge length L = 160 pm. A square probe is centered at xy coordinates (0.100L, 0.900L) and has an x width of 3.00 pm and a y width of 3.00 pm. What is the probability of detection if the electron is in the E, 3 energy state? Probe Number Unitsarrow_forwardThe Potential energy describing a particle of a particle of mass (m) is 00 V(X) = oxx Ka The wave function describing +30 x >a this Particle is Ø = gros exth sincex, where a ² 2mE 2 - a) Apply the boundary condition two find the specific normalized wark function for this particle. MP b) Determine the energy of the first four levels for this particle. c) The Parity of these levels. d) Is. the wif. Continuous. everywhere ? Xarrow_forwardTwo identical non-interacting particles of rest energy 0.1973 MeV are trapped in the same infinitely deep one- dimensional square well of width 0.625 µm. If the total energy of the two-particle state is 0.31568 ueV, write down the two-particle wave function in each of the following cases: a, the particles are spinless; b. the particles are electrons and the spin of the state is S = 0; c. the particles are electrons and the spin of the state is s = 1; d. When the Coulomb repulsion between the electrons is taken into account in (b) and (c), which spin state will have the lower energy?arrow_forwardElectrons are fired at a rectangular potential energy barrier, once every 197 ms. If the barrier is 2.55 nm thick and has a height that exceeds the energy of the incident electrons by exactly 762 meV, how long on average would you expect to wait for one electron to pass through the barrier? average wait: 19.38 x105 Incorrectarrow_forwardA proton is confined to moving in a one- dimensional box 0.2 nm wide. a) Determine the lowest possible proton energy.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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