Physics 2056     Assignment # 4W     Due:   3 April 2003

 

 

  1. Using the notation described in your textbook (1s22s2, etc.) write down the electronic configuration for (a) Ca and (b) As.

 

SOLUTION

 

(a)   Ca: 1s22s22p63s23p64s2

 

(b) As: 1s22s22p63s23p64s23d104p3

 

 

  1. Write down the possible sets of the four quantum numbers when the principal quantum number n = 3.

 

SOLUTION

 

n                l                       ml                    ms

3                0                      0                      +/- ½

3                1                      1                      +/- ½

3                1                      0                      +/- ½

3                1                      -1                     +/- ½

3                2                      2                      +/- ½

3                2                      1                      +/- ½

3                2                      0                      +/- ½

3                2                      -1                     +/- ½

3                2                      -2                     +/- ½

 

 

  1. List the possible sets of quantum numbers for electrons in (a) the 3d subshell and (b) the 3p subshell.

 

SOLUTION

 

(a)   3d: (n = 3, l = 2)

 

n                l                       ml                    ms

3                2                      2                      +/- ½

3                2                      1                      +/- ½

3                2                      0                      +/- ½

3                2                      -1                     +/- ½

3                2                      -2                     +/- ½

 

(b)   3p: (n = 3, l = 1)

 

n                l                       ml                    ms

3                1                      1                      +/- ½

3                1                      0                      +/- ½

3                1                      -1                     +/- ½

 

 

 

  1. Calculate the magnitude of the orbital angular momentum for an electron in (a) the 4d state and (b) the 6f state.

 

SOLUTION

 

(a)   4d:

 

(b) 6f:

 

  1. The principal quantum number for an electron in an atom is n = 6, while the orbital magnetic quantum number is ml = 2.  What possible values for the orbital quantum number l could this electron have?

 

SOLUTION

 

 

  1. An electron in an atom has a value for the orbital magnetic quantum number of ml = 4.  What are the minimum values that (a) the orbital quantum number and (b) the principal quantum number can have?

 

SOLUTION

 

(a)

 

(b)

 

  1. For an electron in a hydrogen atom, the z component of the angular momentum has a maximum value of Lz = 2.11 x 10-34 J·s.  Find the three smallest possible values (algebraically) for the total energy (in eV) that this atom could have.

 

SOLUTION

 

 

 

  1. For the hydrogen atom, the Bohr model and quantum mechanics both give the same value for the energy of the nth state.  However, they do not give the same value for the orbital angular momentum L.  (a) For n = 1, determine the values of L (in units of h/2π) predicted by the Bohr model and quantum mechanics.  (b) Repeat part (a) for n = 2, noting that quantum mechanics permits more than one value of l when the electron is in the n = 2 state.

 

SOLUTION

 

(a)   Bohr ; 

Q. M.

(b)   Bohr ; 

Q. M. ; 

 

  1. Suppose the ionization energy of an atom is 4.10 eV.  In the spectrum of this same atom, we observe emission lines with wavelengths 310 nm, 400 nm and 1378 nm.  Use this information to construct the energy-level diagram with the fewest levels.  Assume that the higher levels are closer together.

 

SOLUTION

 


n = 2
 
                    

n = 1
 
 


           

  1. In x-ray production, electrons are accelerated through a high voltage ΔV and then decelerated by striking a target.  Show that the shortest-wavelength x-ray that can be produced is

 

 

      SOLUTION