Carry out the following conversions. Enter your answer in scientific notation. (a) 232 amu to...

Question:

Carry out the following conversions. Enter your answer in scientific notation.

(a) 232 amu to grams

(b)135 amu to kilograms

(c)3.03 amu A to meters

(d) 3.19 A to nanometers

Conversion of Atomic Mass Unit:

We'll use the general relation between one atomic mass unit and grams shown below to get the required value.

  • {eq}\displaystyle 1\ amu= 1.67377\times 10^{-24}\ grams {/eq}

After that, we'll use the relation between angstrom, meters, and nanometers to compute the unit conversions.

  • {eq}\displaystyle 1 A^{\circ}=1\times 10^{-10}\ meters\\ 1 \ nanometer=1\times 10^{-9}\ meter {/eq}

Answer and Explanation:

(a)

The given value in the atomic mass unit is:

{eq}m=232 amu {/eq}

Multiplying the above value by {eq}1.67377\times 10^{-24}\ grams {/eq}, we get:

{eq}\begin{align*} \displaystyle m&=232 \times 1.67377\times 10^{-24}\ grams\\ &=388.31464\times 10^{-24}\ grams\\ &\approx 3.88\times 10^{-22}\ grams\\ \end{align*} {/eq}


(b)

The given value in the atomic mass unit is:

{eq}m=135 amu {/eq}

Multiplying the above value by {eq}1.67377\times 10^{-24}\ grams {/eq}, we get:

{eq}\begin{align*} \displaystyle m&=135 \times 1.67377\times 10^{-24}\ grams\\ &=255.95895\times 10^{-24}\ grams\\ &\approx 2.56\times 10^{-22}\ grams\\ \end{align*} {/eq}


Converting the above value in kilograms, we get:

{eq}\begin{align*} \displaystyle m&= 2.56\times 10^{-22}\times 10^{-3}\ kilograms\\ &= 2.56\times 10^{-22-3}\ kg\\ &= 2.56\times 10^{-25}\ kg\\ \end{align*} {/eq}


(c)

The given value in angstrom is:

{eq}d=3.03 A^{\circ} {/eq}

Multiplying the above value by {eq}1\times 10^{-10}\ m {/eq}, we get:

{eq}\begin{align*} \displaystyle d&=3.03 \times 1\times 10^{-10}\ m\\ &=3.03\times 10^{-10}\ m\\ \end{align*} {/eq}


(d)

The given value in angstrom is:

{eq}d= 3.19 A^{\circ} {/eq}

Multiplying the above value by {eq}1\times 10^{-10}\ m {/eq}, we get:

{eq}\begin{align*} \displaystyle d&=3.19 \times 1\times 10^{-10}\ m\\ &=3.19\times 10^{-10}\ m\\ \end{align*} {/eq}


Rearranging the expression {eq}1 \ nanometer=1\times 10^{-9}\ meter {/eq}, we get:

{eq}\begin{align*} \displaystyle 1 \ meter&=\frac{1}{10^{-9}} \ nanometer\\ \displaystyle 1 \ meter&=1\times 10^{9} \ nanometer\\ \end{align*} {/eq}


Multiplying the value {eq}3.19\times 10^{-10}\ m {/eq} by the {eq}1\times 10^{9} \ nanometer {/eq}, we get:

{eq}\begin{align*} \displaystyle 3.19\times 10^{-10}\times 1\times 10^{9} \ nanometer&=3.19\times 10^{-10+9} \ nm\\ &=3.19\times 10^{-1} \ nm\\ \end{align*} {/eq}


Learn more about this topic:

Loading...
Common Unit Conversions

from Business 110: Business Math

Chapter 1 / Lesson 10
19K

Related to this Question

Explore our homework questions and answers library