In x-ray studies of crystalline peptides, Linus Pauling and Robert Corey found that the C—N bond in the peptide link is intermediate in length (1.32 Å) between a typical C—N single bond (1.49 Å) and a C=N double bond (1.27 Å). They also found that the peptide bond is planar (all four atoms attached to the C—N group are located in the same plane) and that the two α-carbon atoms attached to the C—N are always trans to each other (on opposite sides of the peptide bond). Required:
a. What does the length of the C—N bond in the peptide linkage indicate about its strength and its bond order (i. e., whether it is single, double, or triple)?
b. What do the observations of Pauling and Corey tell us about the ease of rotation about the C—N peptide bond?

The C-N bond is a double bond.

There is no free rotation about the C-N bond

Explanation:

Linus Pauling and Robert Corey carried out a painstaking study of the bond lengths of peptide bonds as well as the stereo chemistry of atoms and groups around the peptide bonds in the crystal structures of molecules containing one or a few peptide bonds.

Their findings indicate that the bond length of the C-N bond in crystalline peptides is intermediate in length (1.32 Å) between a typical C—N single bond (1.49 Å) and a C=N double bond (1.27 Å). This is because the peptide bond has some double bond character as a result of resonance involving the C=O and -NH moieties of the amide.

As a result of resonance as shown above, the peptide bonds are found to be planar hence free rotation about the C-N bond is hindered. The peptide bond is mostly found in the trans configuration because it is more energetically favourable than the cis configuration.

Summarily, owing to the existence of a partial double bond character between the α carbon and the amine nitrogen in the peptide, there is no free rotation around the C-N bond.

assuming that your periodic table has eighteen columns, you should highlight   the four elements in the third column from the left of the table.

neutral atoms of elements after calcium contain d electrons. the energy of d orbitals of a particular main shell lies between the energy of the s and p orbitals of the next main shell. for example, electrons in the have energy higher than those in the orbital while lower than those of the orbital.

by the aufbau principle, electrons fill orbitals one at a time, starting from those of the lowest energy. the orbital is therefore filled right after orbitals and before orbitals.  

potassium has electron configuration and calcium . the s orbital of a main shell holds a maximum of two electrons. the next element would thus have the electron configuration and satisfy the requirements.

a neutral atom of the element contains three electrons on top of the most recent noble gas element. it should thus be placed in the third column of the periodic table. both scandium and yttrium would satisfy the conditions. an aufbau diagram indicates that the 4f orbital is filled before the 5d. however, it appears that exceptions exists for both lanthanum and actinium. neutral atoms of the two d-block elements also demonstrate the and should be highlighted as well.