Chapter 13, Problem 58P

(a)

To determine

To Calculate:The rms of the amino acid.

Answer to Problem 58P

The rms of the amino acid is $2.9\times {10}^2\text{m/s}$ .

Explanation of Solution

Given:

Molecular mass of the amino acid is $89\text{u}$ .

$T={37}^0\text{C}=\text{310}\text{K}$

Formula used:

  $v_{rms}=\sqrt{\frac{3kT}{m}}$

Here,

$k$ is boltzmann constant,

$T$ is temperature in $\text{K}$ ,

  $m$ is mass of molecule.

Calculation:

For the amino acid

  $\begin{array}{l}{v}_{rms}=\sqrt{\frac{3kT}{m}}\\ v_{rms}=\sqrt{\frac{3kT}{m}}=\sqrt{\frac{3(1.38\times {10}^{-23}\text{J/K})(310\text{K})}{89(1.66\times {10}^{-27}\text{kg})}}\\ =2.9\times {10}^2\text{m/s}\end{array}$

Conclusion:

The root mean square value of the amino acid $2.9\times {10}^2\text{m/s}$ .

(b)

To determine

To Calculate:The root mean square value for the protein.

Answer to Problem 58P

The root mean square value for the protein is $12\text{m/s}$ .

Explanation of Solution

Given:

Molecular mass of the amino acid is $50000\text{u}$ .

$T={37}^0\text{C}=\text{310}\text{K}$

Formula used:

  $v_{rms}=\sqrt{\frac{3kT}{m}}$

Here,

$k$ is boltzmann constant,

$T$ is temperature in $\text{K}$ ,

  $m$ is mass of molecule.

Calculation:

  $\begin{array}{l}{v}_{rms}=\sqrt{\frac{3kT}{m}}\\ =\sqrt{\frac{3(1.38\times {10}^{-23}\text{J/K})(310\text{K})}{50000(1.66\times {10}^{-27}\text{kg})}}\\ =12\text{m/s}\end{array}$

Conclusion:

The root mean square value for the protein $12\text{m/s}$ .