According to the Aufbau principle, the 4s orbital is filled before the 3d orbital for a ground state atom. Use the plot to the right to justify why this is so. 0.2 aor R(r) (Radial Probability Density) 0.18 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 0 5 3d 10 15 4s 30 20 25 r/a, (a in angstroms) 35 40

According to the Aufbau principle, the 4s orbital is filled before the 3d orbital for a ground state atom. Use the plot to the right to justify why this is so. 0.2 aor R(r) (Radial Probability Density) 0.18 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 0 5 3d 10 15 4s 30 20 25 r/a, (a in angstroms) 35 40

Chemistry for Engineering Students

4th Edition

ISBN:9781337398909

Author:Lawrence S. Brown, Tom Holme

Publisher:Lawrence S. Brown, Tom Holme

Chapter6: The Periodic Table And Atomic Structure

Section: Chapter Questions

Problem 6.96PAE: 6.96 When a helium atom absorbs light at 58.44 nm, an electron is promoted from the 1s orbital to a...

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6.32 What are the mathematical origins of quantum numbers?
• identify an orbital (as 1s, 3p, etc.) from its quantum numbers, or vice versa.
Use the mathematical expression for the 2pz wave function of a one-electron atom (see Table 5.2) to show that the probability of finding an electron in that orbital anywhere in the x-y plane is 0. What are the nodal planes for a dxz orbital and for a dx2y2 orbital?
As the weapons officer aboard the Srarship Chemistry, it is your duty to configure a photon torpedo to remove an electron from the outer hull of an enemy vessel. You know that the work function (the binding energy of the electron) of the hull of the enemy ship is 7.52 1019 J. a. What wavelength does your photon torpedo need to be to eject an electron? b. You find an extra photon torpedo with a wavelength of 259 nm and fire it at the enemy vessel. Does this photon torpedo do any damage to the ship (does it eject an electron)? c. If the hull of the enemy vessel is made of the element with an electron configura tion of [Ar]4s13d10, what metal is this?
What experimental evidence supports the quantum theory of light? Explain the wave-particle duality of all matter .. For what size particles must one consider both the wave and the particle properties?
Investigating Energy Levels Consider the hypothetical atom X that has one electron like the H atom but has different energy levels. The energies of an electron in an X atom are described by the equation E=RHn3 where RH is the same as for hydrogen (2.179 1018 J). Answer the following questions, without calculating energy values. a How would the ground-state energy levels of X and H compare? b Would the energy of an electron in the n = 2 level of H be higher or lower than that of an electron in the n = 2 level of X? Explain your answer. c How do the spacings of the energy levels of X and H compare? d Which would involve the emission of a higher frequency of light, the transition of an electron in an H atom from the n = 5 to the n = 3 level or a similar transition in an X atom? e Which atom, X or H, would require more energy to completely remove its electron? f A photon corresponding to a particular frequency of blue light produces a transition from the n = 2 to the n = 5 level of a hydrogen atom. Could this photon produce the same transition (n = 12 to n = 5) in an atom of X? Explain.
6.96 When a helium atom absorbs light at 58.44 nm, an electron is promoted from the 1s orbital to a 2p orbital. Given that the ionization energy of (ground state) helium is 2372 kJ/ mol, find the longest wavelength of light that could eject an electron from the excited state helium atom.
The table below is partially completed for subshells A and B, where subshell B is the next subshell higher in energy compared to subshell A. For example, if subshell A is the 4s subshell, then subshell B would be the 3d subshell. Use this criteria and the information provided to complete the table.
6.93 A mercury atom is initially in its lowest possible (or ground state) energy level. The atom absorbs a photon with a wavelength of 185 nm and then emits a photon with a frequency of 4.9241014HZ . At the end of this series of transitions, the atom will still be in an energy level above the ground state. Draw an energy-level diagram for this process and find the energy of this resulting excited state, assuming that we assign a value of E = 0 to the ground state. (This choice of E = 0 is not the usual convention, but it will simplify the calculations you need to do here.)
In 1885, Johann Balmer, a mathematician, derived the following relation for the wavelength of lines in the visible spectrum of hydrogen =364.5 n2( n2 4) where in nanometers and n is an integer that can be 3, 4, 5, . . . Show that this relation follows from the Bohr equation and the equation using the Rydberg constant. Note that in the Balmer series, the electron is returning to the n=2 level.
Imagine a world in which the rule for the l quantum number is that values start with 1 and go up to n. The rules for the n and mi quantum numbers are unchanged from those of our world. Write the quantum numbers for the first two shells (i.e., n = 1 and n = 2).
Give the possible values of a. the principal quantum number, b. the angular momentum quantum number, c. the magnetic quantum number, and d. the spin quantum number.