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For an atom of mercury, an electron in the
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Chapter 10 Solutions
Physical Chemistry
- 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).arrow_forwardIn 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.arrow_forwardWhat 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?arrow_forward
- 6.32 What are the mathematical origins of quantum numbers?arrow_forwardState how many radial, angular, and total nodes are in each of the following hydrogen-like wavefunctions. a 2s b 3s c 3p d 4f e 6g f 7sarrow_forwardAs 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?arrow_forward
- According to a relationship developed by Niels Bohr, for an atom or ion that has a single electron, the total energy, En, of an electron in a stable orbit of quantum number n is En = [Z2/n2] (2.179 1018 J) where Z is the atomic number. Calculate the ionization energy for the electron in a ground-state He+ ion.arrow_forwardA baseball weighs 142 g. A professional pitcher throws a fast ball at a speed of 100 mph and a curve ball at 80 mph. What wavelengths are associated with the motions of the baseball? If the uncertainty in the position of the ball is 12 wavelength, which ball (fast ball or curve) has a more precisely known position? Can the uncertainty in the position of a curve ball be used to explain why batters frequently miss it?arrow_forwardInvestigating 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.arrow_forward
- 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.)arrow_forward6.92 The photoelectric effect can he used to measure the value of Planck's constant. Suppose that a photoelectric effect experiment was carried out using light with v=7.501014s1 and ejected electrons were detected with a kinetic energy of 2.501011 J. The experiment was then repeated using light with v=1.001015s1 and the same metal target, and electrons were ejected with kinetic energy of 5.001011 J. Use these data to find a value for Planck’s constant. HINTS: These data are fictional and will give a result that is quite different from the real value of Planck's constant. Be sure that you do not use the real value of Planck's constant in any calculations here. It may help to start by thinking about how you would calculate the metal's binding energy if you already knew Planck's constant.arrow_forwardA bright violet line occurs at 435.8 nm in the emission spectrum of mercury vapor. What amount of energy, in joules, must be released by an electron in a mercury atom to produce a photon of this light?arrow_forward
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