A sodium atom (Z = 11) contains 11 protons in its nucleus. Strictly speaking, th

Question

A sodium atom (Z = 11) contains 11 protons in its nucleus. Strictly speaking, the Bohr model does not apply, because the neutral atom contains 11 electrons instead of a single electron. However, we can apply the model to the outermost electron as an approximation, provided that we use an effective value -Z effective father than 11 for the number of protons in the nucleus, (a) The ionization energy for the outermost electron in a sodium atom is 5.1 eV. Use the Bohr model with Z = Z effective to calculate a value for Z effective. (b) Using Z = 11, determine the corresponding value for the radius r of the outermost Bohr orbit, (c) Using the value calculated for Z effective in part (a), determine the corresponding radius r of the outermost Bohr orbit.

Explanation / Answer

a) assuming n=3 and given E=5.1eV
E=-(13.6)Z2/n2      Z=1.837

b) rn= (5.29*10-11m) n2/Z   (z=11and n=3)

r=4.328*10-11m

c) rn= (5.29*10-11m) n2/Z (Z=1.837 from (a) and n=3)

r= 2.591*10-10m

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