Physics for Scientists and Engineers with Modern, Revised Hybrid (with Enhanced WebAssign Printed Access Card for Physics, Multi-Term Courses)
9th Edition
ISBN: 9781305266292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 42, Problem 88AP
To determine
The probability of finding the electron farther than
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where ?∞ = 1.097 × 10^7 m−1is the Rydberg constant and ? is the atomic number (thenumber of protons found in the nucleus). Calculate the ground state energy of a triplyionised beryllium atom, Be3+ (a beryllium atom with three electrons removed).
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Chapter 42 Solutions
Physics for Scientists and Engineers with Modern, Revised Hybrid (with Enhanced WebAssign Printed Access Card for Physics, Multi-Term Courses)
Ch. 42.3 - Prob. 42.1QQCh. 42.3 - Prob. 42.2QQCh. 42.4 - Prob. 42.3QQCh. 42.4 - Prob. 42.4QQCh. 42.8 - Prob. 42.5QQCh. 42 - Prob. 1OQCh. 42 - Prob. 2OQCh. 42 - Prob. 3OQCh. 42 - Prob. 4OQCh. 42 - Prob. 5OQ
Ch. 42 - Prob. 6OQCh. 42 - Prob. 7OQCh. 42 - Prob. 8OQCh. 42 - Prob. 9OQCh. 42 - Prob. 10OQCh. 42 - Prob. 11OQCh. 42 - Prob. 12OQCh. 42 - Prob. 13OQCh. 42 - Prob. 14OQCh. 42 - Prob. 15OQCh. 42 - Prob. 1CQCh. 42 - Prob. 2CQCh. 42 - Prob. 3CQCh. 42 - Prob. 4CQCh. 42 - Prob. 5CQCh. 42 - Prob. 6CQCh. 42 - Prob. 7CQCh. 42 - Prob. 8CQCh. 42 - Prob. 9CQCh. 42 - Prob. 10CQCh. 42 - Prob. 11CQCh. 42 - Prob. 12CQCh. 42 - Prob. 1PCh. 42 - Prob. 2PCh. 42 - Prob. 3PCh. 42 - Prob. 4PCh. 42 - Prob. 5PCh. 42 - Prob. 6PCh. 42 - Prob. 7PCh. 42 - Prob. 8PCh. 42 - Prob. 9PCh. 42 - Prob. 10PCh. 42 - Prob. 11PCh. 42 - Prob. 12PCh. 42 - Prob. 13PCh. 42 - Prob. 14PCh. 42 - Prob. 15PCh. 42 - Prob. 16PCh. 42 - Prob. 17PCh. 42 - Prob. 18PCh. 42 - Prob. 19PCh. 42 - Prob. 20PCh. 42 - Prob. 21PCh. 42 - Prob. 23PCh. 42 - Prob. 24PCh. 42 - Prob. 25PCh. 42 - Prob. 26PCh. 42 - Prob. 27PCh. 42 - Prob. 28PCh. 42 - Prob. 29PCh. 42 - Prob. 30PCh. 42 - Prob. 31PCh. 42 - Prob. 32PCh. 42 - Prob. 33PCh. 42 - Prob. 34PCh. 42 - Prob. 35PCh. 42 - Prob. 36PCh. 42 - Prob. 37PCh. 42 - Prob. 38PCh. 42 - Prob. 39PCh. 42 - Prob. 40PCh. 42 - Prob. 41PCh. 42 - Prob. 43PCh. 42 - Prob. 44PCh. 42 - Prob. 45PCh. 42 - Prob. 46PCh. 42 - Prob. 47PCh. 42 - Prob. 48PCh. 42 - Prob. 49PCh. 42 - Prob. 50PCh. 42 - Prob. 51PCh. 42 - Prob. 52PCh. 42 - Prob. 53PCh. 42 - Prob. 54PCh. 42 - Prob. 55PCh. 42 - Prob. 56PCh. 42 - Prob. 57PCh. 42 - Prob. 58PCh. 42 - Prob. 59PCh. 42 - Prob. 60PCh. 42 - Prob. 61PCh. 42 - Prob. 62PCh. 42 - Prob. 63PCh. 42 - Prob. 64PCh. 42 - Prob. 65APCh. 42 - Prob. 66APCh. 42 - Prob. 67APCh. 42 - Prob. 68APCh. 42 - Prob. 69APCh. 42 - Prob. 70APCh. 42 - Prob. 71APCh. 42 - Prob. 72APCh. 42 - Prob. 73APCh. 42 - Prob. 74APCh. 42 - Prob. 75APCh. 42 - Prob. 76APCh. 42 - Prob. 77APCh. 42 - Prob. 78APCh. 42 - Prob. 79APCh. 42 - Prob. 80APCh. 42 - Prob. 81APCh. 42 - Prob. 82APCh. 42 - Prob. 83APCh. 42 - Prob. 84APCh. 42 - Prob. 85APCh. 42 - Prob. 86APCh. 42 - Prob. 87APCh. 42 - Prob. 88APCh. 42 - Prob. 89CPCh. 42 - Prob. 90CPCh. 42 - Prob. 91CP
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- The distance r between the electron and the nucleus in a hydrogenatom (in its lowest energy state) is a random variable with probability density p(r) = 4a03r2e- 2r/ao for r > 0, where ao is the Bohr radius (Figure 8). Calculate the probability P that the electron is within one Bohrradius of the nucleus. The value of a0 is approximately 5.29 x 10- 11 m,but this value is not needed to compute P.arrow_forwardAssume that the nucleus of an atom can be regarded as a three-dimensional box of width 2:10-¹4 m. If a proton moves as a particle in this box, find (a) the ground-state energy of proton in MeV and (b) the energies of the first excited state. (c) What are the degenerates of these states? Constants: h = 6.626-10-34 [J-s], m = 1.673-10-27 [kg] and ħ=h/2π.arrow_forward7-13. For € = 2, (a) what is the minimum value of L + L3? (b) What is the maximum value of L + L3? (c) What is L + L for € = 2 and m= 1? Can either L, or L, be deter- mined from this? (d) What is the minimum value of n that this state can have?arrow_forward
- One of the bound states of positronium has a lifetime given in natural units by T = 2/mas where m is the mass of the electron and a is the fine structure con- stant. Using dimensional arguments introduce the factors ħ and c and determine T in seconds.arrow_forwardThe total probability of finding an electron in the hydrogen atom is related to the integral ∫ r2 e-2r/ao dr Where r is the distance of the electron from the nucleus and ao is the Bohr radius. Evaluate thisintegral.arrow_forwardAn electron is in a three-dimensional box with side lengths LX = 0.600 nm and LY = LZ = 2LX. What are the quantum numbers nX, nY, and nZ and the energies, in eV, for the four lowest energy levels? What is the degeneracy of each (including the degeneracy due to spin)?arrow_forward
- One can now use integrated-circuit technology to manufacture a "box" that traps electrons in a region only a few nanometers wide. Imagine that we make an essentially one-dimensional box with a length of 3 nanometers. Suppose we put 10 electrons in such a box and allow them to settle into the lowest possible energy states consistent with the Pauli exclusion principle. a) What will be the value of the highest energy level occupied by at least one electron? b) What will be the electrons' total energy (ignoring their electrostatic repulsion)? c) How would your answers to the above be different if the electrons were bosons instead of fermions? d) What is the wavelength of the lowest energy photon that can be absorbed (the electrons in this box are fermions)?arrow_forwardProblem 7: The electric potential near a hydrogen atom can be modeled as the equation to the right where ao is the Bohr radius and q is the charge on the central proton. V (r) exp(- 2r/a,)(1 +a/r) Randomized Variables m = 2 n = 3 Part (a) Find an expression for the 0-component of the electric field, Eg. Numeric : A numeric value is expected and not an expression. Eg = Part (b) Find an expression for the o-component (azimuthal) of the electric field, Eo Expression : Select from the variables below to write your expression. Note that all variables may not be required. a, B, 0, a, b, c, d, g, h, j, k, m, P, S, t Part (c) What is the change in the magnitude of the electric field (in N/C) if a test point moves from the position (x = m²ao, y = 0, z = 0) to position (x = n-ao, y = 0, z = 0). Numeric : A numeric value is expected and not an expression. ΔΕ Ξarrow_forwardIf elements beyond Z = 120 are ever synthesized, electrons in these heavy atoms will begin filling a g subshell, corresponding to l = 4. How many states will be in a g subshell?arrow_forward
- (a) How much energy is required to cause an electron in hydrogen to move from the n = 2 state to the n = 5 state? in J(b) Suppose the atom gains this energy through collisions among hydrogen atoms at a high temperature. At what temperature would the average atomic kinetic energy 3/2 * kBT be great enough to excite the electron? Here kB is Boltzmann's constant. in Karrow_forwardAtomic spectra exist because electrons can only transition between well- defined energy levels, and emit photons with those energies. O True O Falsearrow_forward(a) How much energy is required to cause an electron in hydrogen to move from the n = 2 state to the n = 5 state?in J(b) Suppose the atom gains this energy through collisions among hydrogen atoms at a high temperature. At what temperature would the average atomic kinetic energy 3/2 * kBT be great enough to excite the electron? Here kB is Boltzmann's constant. in Karrow_forward
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