Electronic Structure of Atoms

 

The following problems are taken from T. L. Brown, H. E. Lemay, B. E. Bursten, & J. R. Burdge, Chemistry: The Central Science, Ninth Edition, Chapter 6.

 

22) It requires a photon with a minimum energy of 4.41 x 10-19 J to emit electrons from sodium metal.

      (a) What is the minimum frequency of light necessary to emit electrons from sodium via the photoelectric effect?

      (b) What is the wavelength of this light?

      (c) If sodium is irradiated with light of 439 nm, what is the maximum possible kinetic energy of the emitted electrons?

      (d) What is the maximum number of electrons that can be freed by a burst of light whose total energy is 1.00 µJ?

                    

28) For each of the following electronic transitions in the hydrogen atom, calculate the energy, frequency, and wavelength of the associated radiation, and determine whether the radiation is emitted or absorbed during the transition:

      (a) from n = 5 to n = 1

      (b) from n = 4 to n = 2

      (c) from the n = 4 to n = 6

      (d) Does any of these transitions emit or absorb visible light?

      

38) Calculate the uncertainty in the position of:

      (a) an electron moving at a speed of (3.00 ± 0.01) x 105 m/s

      (b) a neutron moving at this same speed

      (c) What are the implications of these calculations to our model of the atom?

     
46) Which of the following are permissable sets of quantum numbers for an electron in a hydrogen atom: 

      (a) n = 2, l = 1, ml = 1

      (b) n = 1, l = 0, ml = -1

      (c) n = 4, l = 2, ml = -2

      (d) n = 3, l = 3, ml = 0     

      For those combinations that are permissable, write the appropriate designation for the subshell to which the orbital belongs (that is, 1s, and so on).

      

56) What is the maximum number of electrons in an atom that can have the following quantum numbers:

      (a) n = 2, ms = -1/2,

      (b) n = 5, l = 3

      (c) n = 4, l = 3, ml = -3

      (d) n = 4, l = 1, ml = 1

      

74) The light-sensitive substance in black-and-white photographic film is AgBr. Photons provide the energy necessary to transfer an electron from Br- to Ag+ to produce Ag and Br and thereby darken the film.

      (a) If a minimum energy of 2.00 x 105 J/mol is needed for this process, what is the minimum energy needed by each photon?

      (b) Calculate the wavelength of the light necessary to provide photons of this energy.

      (c) Explain why this film can be handled in a dark room under red light.