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- The amount of energy necessary to remove an electron from an atom is a quantity called the ionization energy, Ei. This energy can be measured by a technique called photoelectron spectroscopy, in which light of wavelength l is directed at an atom, causing an electron to be ejected. The kinetic energy of the ejected electron (Ek) is measured by determining its veloc-ity, v (Ek = mv2/2), and Ei is then calculated using the conservation of energy principle. That is, the energy of the incident light equals Ei plus Ek. What is the ionization energy of selenium atoms in kilojoules per mole if light with l = 48.2 nm produces electrons with a velocity of 2.371 * 106 m/s? The mass, m, of an electron is 9.109 * 10-31 kg.
Problem 132
- X rays with a wavelength of 1.54 * 10-10 m are produced when a copper metal target is bombarded with high-energy electrons that have been accelerated by a voltage difference of 30,000 V. The kinetic energy of the electrons equals the product of the voltage difference and the electronic charge in coulombs, where 1 volt-coulomb = 1 J. (a) What is the kinetic energy in joules and the de Broglie wavelength in meters of an electron that has been accel-erated by a voltage difference of 30,000 V?
Problem 133
- In the Bohr model of atomic structure, electrons are constrained to orbit a nucleus at specific distances, given by the equation
Problem 134
where r is the radius of the orbit, Z is the charge on the nucleus, a0 is the Bohr radius and has a value of 5.292 * 10-11 m, and n is a positive integer (n = 1, 2, 3...) like a principal quantum number. Furthermore, Bohr concluded that the energy level E of an electron in a given orbit is
where e is the charge on an electron. Derive an equation that will let you calculate the difference ∆E between any two energy levels. What relation does your equation have to the Balmer–Rydberg equation?
- Assume that the rules for quantum numbers are different and that the spin quantum number ms can have any of three values, ms = -1/2, 0, +1/2, while all other rules remain the same. (a) Draw an orbital-filling diagram for the element with Z = 25, showing the individual electrons in the outer-most subshell as up arrows, down arrows, or 0. How many partially filled orbitals does the element have?
Problem 135
Problem 136a
A minimum energy of 7.21⨉10-19 J is required to produce the photoelectric effect in chromium metal. (a) What is the minimum frequency of light needed to remove an electron from chromium?
Problem 136b
A minimum energy of 7.21⨉10-19 J is required to produce the photoelectric effect in chromium metal. (b) Light with a wavelength of 2.50⨉10-7 m falls on a piece of chromium in an evacuated glass tube. What is the minimum de Broglie wavelength of the emitted electrons? (Note that the energy of the incident light must be conserved; that is, the photon's energy must equal the sum of the energy needed to eject the electron plus the kinetic energy of the electron.)
- (c) What is the velocity of an electron with a de Broglie wavelength equal to (b)?
Problem 137
Problem 138b
An energetically excited hydrogen atom has its electron in a 5f subshell. The electron drops down to the 3d subshell, releasing a photon in the process. (b) What wavelength of light is emitted by the process?
Problem 138c
An energetically excited hydrogen atom has its electron in a 5f subshell. The electron drops down to the 3d subshell, releasing a photon in the process. (c) The hydrogen atom now has a single electron in the 3d subshell. What is the energy in kJ/mol required to remove this electron?
Problem 139a
Consider the noble gas xenon. (a) Write the electron configuration of xenon using the abbreviation of the previous noble gas.
Problem 139c
Consider the noble gas xenon. (c) The energy required to completely remove the outermost electron from the excited xenon atom is 369 kJ/mol, almost identical to that of cesium (376 kJ/mol). Explain.
- Red light with a wavelength of 660 nm from a 3.0 mW diode laser shines on a solar cell. (b) How much current (in amperes) flows in the circuit of the solar cell if all the photons are absorbed by the cell and each photon produces one electron?
Problem 140