Q78E - Chemistry (OpenStax)

Question

Question:  Many chemistry conferences have held a 50-Trillion Angstrom Run (two significant figures). How long is thisrun in kilometers and in miles? (1 Å = 1 × 10⁻¹⁰ m)

Step-by-Step Solution

Answer

A 50 trillion Angstrom in kilometers and miles is 5.0 km and 3.1 miles, respectively.

Step 1: Defining the 50 trillion Angstrom run

A trillion is a number which is one million million, .i.e., 10¹².

\(1\,\,trillion\,\, = \,\,1\,\, \times \,\,{10^{12}}\)

But we have 50 trillion.

\(50\,trillion\,\, = \,\,50\, \times \,\,{10^{12}}\)

Now we know that

Angstrom is the unit of length for smaller species or substances. It is denoted by\(\mathop A\limits^o \).

\(1\,\,\mathop A\limits^o \,\, = \,\,1\,\, \times \,\,{10^{ - 10}}\,m\)

Step 2: Converting the quantity into kilometres and miles

Here, merging the above quantities, we get

So, \(\begin{array}{c}50\,\,trillion\,Angstrom\,\, = \,\,\,50\,\, \times \,\,{10^{12}}\, \times \,{10^{ - 10}}\,m\,\,\\ = \,\,5000\,\,m\,\,\\ = \,\,5\,\,km\end{array}\)

Therefore, 50 trillion Angstrom is 5.0 km or 5000 m.

Also, we know that

\(1\,\,mile\,\, = \,\,1.61\,\,km\)

Using the above conversion factor,

\(\begin{array}{c}5\,\,km\,\, = \,\,5\,\,km\,\, \times \,\frac{{mile}}{{1.61\,\,km}}\,\\\, = \,\,3.105\,\,miles\end{array}\)

We have to show it in two significant figures 

Therefore, a 50 trillion Angstrom is 5.0 km and 3.1 miles.