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)

Short answer

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

Step-by-step solution

Defining the 50 trillion Angstrom run

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

$1trillion=1\times {10}^{12}$

But we have 50 trillion.

$50trillion=50\times {10}^{12}$

Now we know that

Angstrom is the unit of length for smaller species or substances. It is denoted by$\stackrel{o}{A}$.

$1\stackrel{o}{A}=1\times {10}^{-10}m$

Converting the quantity into kilometres and miles

Here, merging the above quantities, we get

So, $\begin{array}{c}50trillionAngstrom=50\times {10}^{12}\times {10}^{-10}m\\ =5000m\\ =5km\end{array}$

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

Also, we know that

$1mile=1.61km$

Using the above conversion factor,

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

We have to show it in two significant figures

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