Inquiry into Physics
8th Edition
ISBN: 9781337515863
Author: Ostdiek
Publisher: Cengage
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Chapter 10, Problem 15P
To determine
Smallest value of principle quantum number
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Consider the elements selenium (Z = 34), bromine (Z = 35), and krypton (Z = 36). In their part of the periodic table, the subshells of the electronic states are filled in the sequence 1s 2s 2p 3s 3p 3d 4s 4p . . . . What are (a) the highest occupied subshell for selenium and (b) the number of electrons in it, (c) the highest occupied subshell for bromine and (d) the number of electrons in it, and (e) the highest occupied subshell for krypton and (f) the number of electrons in it?
A hypothetical atom has only two atomic energy levels, separated by 3.2 eV. Suppose that at a certain altitude in the atmosphere of a star there are 6.1 * 1013/cm3 of these atoms in the higher-energy state and 2.5 * 1015/cm3 in the lower-energy state. What is the temperature of the star’s atmosphere at that altitude?
3.
eV.
Consider an atom of triply ionized beryllium Be³+ with an energy of -9.704
(a) List all the possible states, excluding spin, of the hydrogen atom with this energy.
(b) What is the degree of degeneracy?
(c) What is the maximum possible angular momentum L (as a multiple of ħ)?
Chapter 10 Solutions
Inquiry into Physics
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- How many electrons can occupy (a) the 2p subshell and (b) the3p subshell?arrow_forward(a) The Lyman series in hydrogen is the transition from energy levels n = 2, 3, 4, ... to the ground state n = 1. The energy levels are given by 13.60 eV En n- (i) What is the second longest wavelength in nm of the Lyman series? (ii) What is the series limit of the Lyman series? [1 eV = 1.602 x 1019 J, h = 6.626 × 10-34 J.s, c = 3 × 10° m.s] %3D Two emission lines have wavelengts A and + A2, respectively, where AA <<2. Show that the angular separation A0 in a grating spectrometer is given aproximately by (b) A0 = V(d/m)-2 where d is the grating constant and m is the order at which the lines are observed.arrow_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
- Form factor of atomic hydrogen. For the hydrogen atom in its ground state, the number density is n(r) = (7a) exp(-2r/a,), where a, is the Bohr radius. Show that the form factor is fc = 16/(4 + Gʻa)*. %3D %3Darrow_forward9. An atom in a solid has two energy levels: a ground state of degeneracy gi and an excited state of degeneracy g2 with an energy A above the ground state. (a) Show that the partition function for the atom, Zatom; is Zatom = 91 + »e¬ßA (b) Show that the heat capacity of the atom is given by 9192A²e¬BA kgT² (g1 + g2e-BA)² (c) Show that a monatomic gas of these atoms has a partition function of Z = ZatomZN Where only translational motion of the gaseous atoms is considered so that N V ZN =arrow_forward= . Using the formula for the hydrogen atom energy levels, En constant can be written in terms of fundamental quantities, RH = Me 4 8€, ²h³c Me 4 1 860²h² n²¹ the Rydberg and its value approaches, RH → R∞ = 10,973,731.6 m-¹ in the limit u → me. (a) How would this constant be defined for a one-electron species containing Z protons in its nucleus? Consider how this changes the form of the Hamiltonian and the energy levels for that Hamiltonian. (b) The hydrogen atom emission lines in the Balmer series (n₂ = 2) lie in the visible portion of the electromagnetic spectrum. Would this also be true if Z> 1? Find the wavelength (in nm) of the n = 32 emission in hydrogen and that for a one-electron species with Z = 2. (You will be asked to report a quantity on the quiz that depends on these two values.)arrow_forward
- = Using the formula for the hydrogen atom energy levels, En constant can be written in terms of fundamental quantities, RH = Me 4 8€ ²h³c Me4 1 860²h² n²¹ the Rydberg and its value approaches, RH → R = 10,973,731.6 m¹ in the limit μ→ me. (a) How would this constant be defined for a one-electron species containing Z protons in its nucleus? Consider how this changes the form of the Hamiltonian and the energy levels for that Hamiltonian. (b) The hydrogen atom emission lines in the Balmer series (n₂ = 2) lie in the visible portion of the electromagnetic spectrum. Would this also be true if Z> 1? Find the wavelength (in nm) of the n = 32 emission in hydrogen and that for a one-electron species with Z = 2. (You will be asked to report a quantity on the quiz that depends on these two values.)arrow_forwardA hydrogen atom passes through a strong external magnetic field of B= 10 Tesla.A) List the possible quantum states (?, ?, ?l, ?s) for the 3p level.B) Calculate the energies of each of these quantum states.arrow_forwardThe electronic structure of one-dimensional chain of sodium (Na) atoms can be approximately described by the particle-in-a-box model. The energy of each state can be calculated using n²h? En = 5,n = 1,2,3, ... 8mL2 where L is the length of the 1D chain. Assuming L = ao(N – 1), where N is the number of Na atoms and ao = 0.360 nm is the internuclear distance. a) Determine the energy gap between the highest occupied energy level and the lowest unoccupied energy level as a function of N. Assume that N is an even number that is large enougharrow_forward
- a. The electron of a hydrogen atom is excited into a higher energy level from a lower energy level. A short time later the electron relaxes down to the no = 1 energy level, releasing a photon with a wavelength of 93.83 nm. Compute the quantum number of the energy level the electron relaxes from, nhi. Note: the Rydberg constant in units of wavenumbers is 109,625 cm-1 nhi =16 b. What would the wavenumber, wavelength and energy of the photon be if instead no = 1 and nhi = 4? V: 6.9121e14 x (cm-¹) λ: (nm) E: 45.8e-20 ✓ (1)arrow_forwardThe Lyman series comprises a set of spectral lines. All of these lines involve a hydrogen atom whose electron undergoes a change in energy level, either beginning at the n = 1 level (in the case of an absorption line) or ending there (an emission line). The inverse wavelengths for the Lyman series in hydrogen are given by 1 - where n = 2, 3, 4, ... and the Rydberg constant R, = 1.097 x 10' m-. (Round your answers to at least one decimal place. Enter your answers in nm.) %3D (a) Compute the wavelength for the first line in this series (the line corresponding to n = 2). nm (b) Compute the wavelength for the second line in this series (the line corresponding to n = 3). nm (c) Compute the wavelength for the third line in this series (the line corresponding to n = 4). nm (d) In which part of the electromagnetic spectrum do these three lines reside? O x-ray region O ultraviolet region O infrared region O gamma ray region O visible light regionarrow_forwardForm factor of atomic hydrogen. For the hydrogen atom in its ground state, the number density is n(r) = (ra)¯ exp(-2r/a), where a, is the Bohr radius. Show that the form factor is fc = 16/(4 + G*a)*. %3Darrow_forward
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