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Convert 278 amu to grams (Use scientific notation).

Question:

Convert 278 amu to grams (Use scientific notation).

Atomic Mass Unit:

One atomic mass unit is equal to the sum of rest masses of the proton and neutron divided by {eq}2 {/eq}.

We'll multiply the given value by the obtained value of one {eq}1 {/eq} amu to get the exact answer.

Answer and Explanation:

The given value in the atomic mass unit is:

{eq}m=278\ amu {/eq}

The rest mass of the proton is equal to {eq}1.67262\times 10^{-27}\ kg {/eq} and the rest mass of the neutron is equal to {eq}1.67493 \times 10^{-27}\ kg {/eq}.

According to the definition, one atomic mass unit is:

{eq}\begin{align*} \displaystyle 1\ amu&= \frac{1.67262\times 10^{-27}+1.67493 \times 10^{-27}}{2}\\ &= \displaystyle \frac{(1.67262+1.67493) \times 10^{-27}}{2}\\ &= \displaystyle \frac{3.34755 \times 10^{-27}}{2}\\ &=\displaystyle 1.673775\times 10^{-27}\ kg \end{align*} {/eq}


Multiplying the given value by the above value, we get:

{eq}\begin{align*} \displaystyle 278\ amu&=278\times 1.673775\times 10^{-27}\ kg \\ &=465.30945\times 10^{-27}\ kg \end{align*} {/eq}


Multiply the above value by {eq}1000 {/eq} to get the answer in grams.

{eq}\begin{align*} \displaystyle 278\ amu&=465.30945\times 10^{-27}\times 1000\ g \\ &=465.30945\times 10^{-24}\ g \\ &\approx 4.65\times 10^{-22}\ g \\ \end{align*} {/eq}


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Common Unit Conversions

from Business 110: Business Math

Chapter 1 / Lesson 10
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