Question

What is 1 $A^\circ$ equal to:
A. 10nm
B. 0.1nm
C. 100nm
D. 1nm

Answer 1

There are several units named by different scientists to measure lengths. On a macroscopic level, we even have huge astronomical units to measure the distance between planets and the diameter of galaxies for example light years – which means the distance travelled by light in one year. Also on a microscopic or quantum level, we have small units to measure size of electron and radius of nucleus, etc.

Formula used:
1 $A^\circ$= $10^{-10}m$, 1nm = $10^{-9}$m

Complete step-by-step answer:
Let 1 $A^\circ$= N nm. We know, 1 $A^\circ$= $10^{-10}m$& 1nm = $10^{-9}$m.
Putting the known values in the equation:
$10^{-10}m$= N $\times$ $10^{-9}$m
Hence, N =$\dfrac {10^{-10}} {10^{-9}}$= $10^{-1}$=0.1 [$\dfrac {10^{a}} {10^{b}}=10^{a-b}$]
So, 1 $A^\circ$= 0.1 nm

So, the correct answer is “Option B”.

Additional Information:
There are several more units that have very important meaning in physics and chemistry. These are stated as:
1 meter = 100 centimeters
1 millimeter (mm) = 0.001 m
1 meter = 1000 millimeters
1 millimeter (mm) = 0.1 cm
1 centimeter = 10 millimeters
1 micrometer ($\mu$m) = 0.001 mm
1 millimeter = 1000 micrometers
1 nanometer (nm) = 0.001 $\mu$m
1 micrometer = 1000 nanometers
1 kilometer = 1000 m
1 hectometer = 100 m
1 centimeter (cm) = 0.01 m
1 femtometer (fm) = 0.00001$A^\circ$
1 decameter = 10 m
1 Megameter = 1000000 m, etc.

Note: Such conversions are very important to be remembered. Physics is all about information. Remembering these units will make such information of sizes such as size of nucleus, which is of the order of femtometer, easy to remember. For conversion questions, it is preferred to take both side units into S.I. units. The S.I. unit of length is meter (m).