Q79E - Chemistry (OpenStax)

Question

Question:  A chemist’s 50-Trillion Angstrom Run (see Exercise 1.78) would be an archeologist’s 10,900 cubit run. Howlong is one cubit in meters and in feet? (1 Å = 1 × 10^-8 cm)

Step-by-Step Solution

Answer

One cubit is 0.46 m and 1.5 ft long.

Step 1: Defining the Trillion Angstrom and cubit units

We know that one trillion Angstrom is equal to 5 km (from Exercise 1.78).

A cubit is an ancient measure unit. It is measured based on the length between the elbow to the middle finger.

Also, 10,900 cubits are considered 50 Trillion Angstrom.

Step 2: Converting the cubit into meters and feet

We know that

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

And

\(10,900\,\,cubit\,\, = \,\,\,50\,trillion\,\,Angstrom\)

Therefore,

\(10,900\,\,cubit\,\, = \,\,5000\,\,m\)

\(\begin{array}{l}1\,\,cubit\,\, = \,\,\frac{{5000}}{{10,900}}\,\,m\,\,\\1\,\,cubit\,\, = \,\,\,0.4587\,\,m\end{array}\)

Rounding off, we get 0.46 m.

Also, we know

\(1\,\,m\,\, = \,\,3.28\,\,ft\)

We get

\(\begin{array}{c}1\,\,cubit\,\, = \,\,0.4587\,\,m\,\\\, = \,\,1.5049\,\,ft\end{array}\)

Rounding off, we get 1.5 ft.

Therefore, one cubit in meters and feet are 0.46 m and 1.5 ft.