Chapter 1, Problem 39GP

(a)

To determine

To find: The total number of protons or neutrons in a bacterium.

Answer to Problem 39GP

  $n\approx 1.0\times {10}^{12}\text{ protons or nuetrons}$

Explanation of Solution

Given:

Mass of a bacterium, $M={10}^{-15}\text{ kg}$

Mass of proton or neutron, $m=1.67\times {10}^{-27}\text{ kg}$

Formula used:

Number of protons or neutrons:

  $n=\frac{M}{m}$

Where,

  $M=$ Mass of a bacterium

  $m=$ Mass of a proton

  $n=$ Number of protons or neutrons.

Calculation:

Plugging in the given values:

  $\begin{array}{c}n=\frac{{10}^{-15}\text{ kg}}{1.67\times {10}^{-27}\text{ kg}}\\ =0.5988\times {10}^{12}\\ \approx 1.0\times {10}^{12}\text{ protons or nuetrons}\end{array}$

Conclusion:

Hence, number of protons or neutrons in a bacterium: $1.0\times {10}^{12}$

(b)

To determine

To find: The total number of protons or neutrons in a DNA molecule.

Answer to Problem 39GP

  $n\approx 1.0\times {10}^{10}\text{ protons or nuetrons}$

Explanation of Solution

Given:

Mass of a DNA molecule, $M={10}^{-17}\text{ kg}$

Mass of proton or neutron, $m=1.67\times {10}^{-27}\text{ kg}$

Formula used:

Number of protons or neutrons:

  $n=\frac{M}{m}$

Where,

  $M=$ Mass of a DNA molecule.

  $m=$ Mass of a proton

  $n=$ Number of protons or neutrons.

Calculation:

Plugging in the given values:

  $\begin{array}{c}n=\frac{{10}^{-17}\text{ kg}}{1.67\times {10}^{-27}\text{ kg}}\\ =0.5988\times {10}^{10}\\ \approx 1.0\times {10}^{12}\text{ protons or nuetrons}\end{array}$

Conclusion:

Hence, number of protons or neutrons in a DNA molecule: $1.0\times {10}^{10}$

(c)

To determine

To find: The total number of protons or neutrons in a human body.

Answer to Problem 39GP

  $n\approx 1.0\times {10}^{29}\text{ protons or nuetrons}$

Explanation of Solution

Given:

Mass of the human body, $M={10}^2\text{ kg}$

Mass of proton or neutron, $m=1.67\times {10}^{-27}\text{ kg}$

Formula used:

Number of protons or neutrons:

  $n=\frac{M}{m}$

Where,

  $M=$ Mass of the human body.

  $m=$ Mass of a proton

  $n=$ Number of protons or neutrons.

Calculation:

Plugging in the given values:

  $\begin{array}{c}n=\frac{{10}^2\text{ kg}}{1.67\times {10}^{-27}\text{ kg}}\\ =0.5988\times {10}^{29}\\ \approx 1.0\times {10}^{29}\text{ protons or nuetrons}\end{array}$

Conclusion:

Hence, number of protons or neutrons in a human body: $1.0\times {10}^{29}$

(d)

To determine

To find: The total number of protons or neutrons in our galaxy.

Answer to Problem 39GP

  $n\approx 1.0\times {10}^{68}\text{ protons or nuetrons}$

Explanation of Solution

Given:

Mass of our galaxy, $M={10}^{41}\text{ kg}$

Mass of proton or neutron, $m=1.67\times {10}^{-27}\text{ kg}$

Formula used:

Number of protons or neutrons:

  $n=\frac{M}{m}$

Where,

  $M=$ Mass of our galaxy.

  $m=$ Mass of a proton

  $n=$ Number of protons or neutrons.

Calculation:

Plugging in the given values:

  $\begin{array}{c}n=\frac{{10}^{41}\text{ kg}}{1.67\times {10}^{-27}\text{ kg}}\\ =0.5988\times {10}^{68}\\ \approx 1.0\times {10}^{68}\text{ protons or nuetrons}\end{array}$

Conclusion:

Hence, number of protons or neutrons in our galaxy: $1.0\times {10}^{68}$