Ch.5 - Periodicity & Electronic Structure of Atoms
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- Spectroscopy is a technique that uses the interaction of radiant energy with matter to identify or quantify a substance in a sample. A deuterium lamp is often used a light source in the ultraviolet region of the spectrum and the emission spectrum is shown. Is this a continuous or line emission spectrum?
Problem 56
- Sodium-vapor lamps are a common source of lighting. The emission spectrum from this type of lamp is shown. Is this a continuous or line emission spectrum?
Problem 57
- According to the equation for the Balmer line spectrum of hydrogen, a value of n = 3 gives a red spectral line at 656.3 nm, a value of n = 4 gives a green line at 486.1 nm, and a value of n = 5 gives a blue line at 434.0 nm. Calculate the energy in kilojoules per mole of the radiation corresponding to each of these spectral lines.
Problem 58
- Calculate the wavelength and energy in kilojoules necessary to completely remove an electron from the second shell (m = 2) of a hydrogen atom (R∞ = 1.097 * 10-2 nm-1).
Problem 61
- Use the Balmer equation to calculate the wavelength in nano-meters of the spectral line for hydrogen when n = 6 and m = 2. What is the energy in kilojoules per mole of the radiation corresponding to this line?
Problem 64
- Protons and electrons can be given very high energies in particle accelerators. What is the wavelength in meters of an electron (mass = 9.11 * 10-31 kg) that has been accelerated to 5% of the speed of light? In what region of the electromagnetic spectrum is this wavelength?
Problem 66
- What is the de Broglie wavelength in meters of a baseball weighing 145 g and traveling at 156km/h? Why do we not observe this wavelength?
Problem 68
- At what speed in meters per second must a 145 g baseball be traveling to have a de Broglie wavelength of 0.500 nm?
Problem 70
- What velocity would an electron (mass = 9.11 * 10-31 kg) need for its de Broglie wavelength to be that of red light (750 nm)?
Problem 71
- Use the Heisenberg uncertainty principle to calculate the uncertainty in meters in the position of a honeybee weighing 0.68 g and traveling at a velocity of 0.85 m/s. Assume that the uncertainty in the velocity is 0.1 m/s.
Problem 72
- The mass of a helium atom is 4.0026 amu, and its average velocity at 25 °C is 1.36 * 103 m/s. What is the uncertainty in meters in the position of a helium atom if the uncertainty in its velocity is 1%?
Problem 73
- What is the Heisenberg uncertainty principle, and how does it affect our description of atomic structure?
Problem 74
- Why do we have to use an arbitrary value such as 90% to determine the spatial limitations of an orbital?
Problem 75
- What are the four quantum numbers, and what does each specify?
Problem 76
- Tell which of the following combinations of quantum numbers are not allowed. Explain your answers. (a) n = 3, l = 0, ml = -1 (b) n = 3, l = 1, ml = 1 (c) n = 4, l = 4, ml = 0
Problem 77
- Give the allowable combinations of quantum numbers for each of the following electrons. (a) A 4s electron (b) A 3p electron (c) A 5f electron (d) A 5d electron
Problem 78
- Give the orbital designations of electrons with the following quantum numbers. (a) n = 3, l = 0, ml = 0 (b) n = 2, l = 1, ml = -1 (c) n = 4, l = 3, ml = -2 (d) n = 4, l = 2, ml = 0
Problem 79
- What is the maximum number of electrons in an atom whose highest-energy electrons have the principal quantum number n = 5?
Problem 82
- Assign a set of four quantum numbers to each electron in oxygen.
Problem 87
- Assign a set of four quantum numbers for the outermost two electrons in Sr.
Problem 88
- How many nodal surfaces does a 4s orbital have? Draw a cutaway representation of a 4s orbital showing the nodes and the regions of maximum electron probability.
Problem 90
- What do the different colors in the two lobes of the p orbitals specify?
Problem 92
- What is the l quantum of an orbital that has four lobes that resemble a cloverleaf?
Problem 93
- What is meant by the term effective nuclear charge, Z_eff, and what causes it?
Problem 94
- Order the following elements according to increasing Z_eff: Ca, Se, Kr, K.
Problem 97
- Why does the number of elements in successive periods of the periodic table increase by the progression 2, 8, 18, 32?
Problem 98
- Which two of the four quantum numbers determine the energy level of an orbital in a multielectron atom?
Problem 99
- Order the orbitals for a multielectron atom in each of the following lists according to increasing energy. (a) 4d, 3p, 2p, 5s (b) 2s, 4s, 3d, 4p (c) 6s, 5p, 3d, 4p
Problem 101
- According to the aufbau principle, which orbital is filled immediately after each of the following in a multielectron atom? (a) 4s (b) 3d (c) 5f (d) 5p
Problem 102
- According to the Aufbau principle, which orbital is filled immediately before each of the following? (a) 3p (b) 4p (c) 4f (d) 5d
Problem 103