Answer : The length of protein will be, 96.8 A⁰
Explanation :
First we have to calculate the amino acid residue.
![\text{Amino acid residue}=\frac{\text{Length of single strand of protein}}{\text{Mean residue mass}}](https://img.qammunity.org/2021/formulas/chemistry/college/20ztafefr472tgvvef1qfjhpugdrei0gzf.png)
Given:
Length of single strand of protein = 71.0 kDa
Mean residue mass = 110 Da
![\text{Amino acid residue}=(71.0kDa)/(110Da)=(71000Da)/(110Da)=645.4](https://img.qammunity.org/2021/formulas/chemistry/high-school/d3ocb5k36qucpncedbilo4dmpyutp1r4i0.png)
Now we have to calculate the number of turns in protein.
![\text{Number of turns in protein}=\frac{\text{Amino acid residue}}{3.6\text{amino acid per turn of the alpha-helix}}](https://img.qammunity.org/2021/formulas/chemistry/college/ln5e8ws757di916fhoe42qxlrzfwbpt049.png)
As there are 3.6 amino acid per turn of the alpha-helix.
![\text{Number of turns in protein}=(645.4)/(3.6)=179.28](https://img.qammunity.org/2021/formulas/chemistry/high-school/t2dj5q375ga7fsx1yr1vqysy13opgmfuiu.png)
Now we have to calculate the length of the protein.
![\text{Length of protein}=\text{Number of turns in protein}* \text{Length of each turn}](https://img.qammunity.org/2021/formulas/chemistry/college/lgyuslq04yv1764isf9k79makrh5rsu3lj.png)
As, we know that the length of each turn = 0.54 A⁰
![\text{Length of protein}=179.28turns* \0.54\AA=96.8\AA](https://img.qammunity.org/2021/formulas/chemistry/high-school/ldzb9bqfy6eonmgjt9ezrx904j65mk0bkt.png)
Thus, the length of protein will be, 96.8 A⁰