Q40P - Fundamentals Of Physics

Question

Using conversions and data in the chapter, determine the number of hydrogen atoms required to obtain${}^{\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{ }\mathbf{kg}}$ of hydrogen. A hydrogen atom has a mass of ${}^{\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{ }\mathbf{u}}$.

Step-by-Step Solution

Answer

The number of hydrogen atoms required to obtain${}^{\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{ }\mathbf{kg}}$ of hydrogen is${}^{\mathbf{6}\mathbf{.}\mathbf{022}\mathbf{\times }{\mathbf{10}}^{\mathbf{26}}}$

Step 1: Listing the given quantities

Total mass of hydrogen is 1.0 kg.

Mass of one hydrogen atom is ${}^{\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{ }\mathbf{u}}$. 

Step 2: Understanding the unit conversion

Unit conversion is the conversion between different units of measure for the same quantity, usually through multiplier conversion factors. One atomic mass unit is equivalent to $\mathbf{1}\mathbf{.}\mathbf{66054}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{27}}$. Using this conversion factor, find the number of hydrogen atoms in 1 kg of hydrogen.

Step 3: Determination of the number of hydrogen atoms required to obtain 1 . 0   kg of hydrogen

Use the conversion factor to find the number of hydrogen atoms in ${}^{\mathbf{1}\mathbf{ }\mathbf{kg}}$.

$$\begin{gathered} \mathbf{1}\mathbf{ }\mathbf{kg}\mathbf{=}\mathbf{1}\mathbf{ }\mathbf{kg}\mathbf{\times }\frac{\mathbf{1}}{\mathbf{1}\mathbf{.}\mathbf{6605}\mathbf{\times }{\mathbf{10}}^{\mathbf{27}}\mathbf{ }\mathbf{kg}}\mathbf{ }\mathbf{atoms} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{6}\mathbf{.}\mathbf{022}\mathbf{\times }{\mathbf{10}}^{\mathbf{26}}\mathbf{ }\mathbf{atoms} \end{gathered}$$

Thus, ${}^{\mathbf{1}\mathbf{ }\mathbf{kg}}$ hydrogen will have ${}^{\mathbf{6}\mathbf{.}\mathbf{022}\mathbf{\times }{\mathbf{10}}^{\mathbf{26}}\mathbf{ }\mathbf{atoms}}$ .