Diameter of a ground-state hydrogen atom in meters using scientific notation?

Answer 1

To set up this problem in DA, do the following.

0.1nm/atom*10^9m/nm

That is, 0.1 nanometers per atom, times 10−9 meters per nanometer.

By cross-cancelling the units (nanometers on the left side cross-cancels with nanometers on the right side), we end up with units of meters per atom - exactly what you were looking for!

All that's left to do is multiply 0.1 times 10−9, and you should get 10−10.

So the answer is 10−10 meters, which leads to another unit known as the Ångström (Å), which although it is a non-SI unit, it is one of the more common units used when referring to atomic distances. 1 Å = 10−10 m = diameter of hydrogen in its ground state. Thus we have 1Å/atom and 1atom/Å.

Asking how many H-atoms there are in a meter and applying dimensional analysis leads to 1m*(1Å/10−10m)*(1atom/1Å)=1010atoms. (It is easier to see the units cancel one another if you write out the problem in the form of fractions, like in the above tutorial link).

So, one meter is 1010 H-atoms in length! What is amazing is that the official definitions for the meter have never incorporated consideration for the diameter of hydrogen.

Algebraic Steps / Dimensional Analysis Formula 0.1 nm*

1 m

1000000000 nm=1e-10 m

You can answer this (and any problem involving unit conversion) using the conversion factor method, which goes by a variety of other names such as unit-factor method, factor-label method and dimensional analysis. Whatever the name, it is much easier than it sounds.

First off, get acquainted with the metric prefixes- http:/en.wikipedia.org/wiki/SI_prefix

Then check out this nice little tutorial (no affilliation)-

http:/www.lynchburg.net/hhs/chemistry/dozens/cfactor.htm

As you can see from the first link above, one nanometer is equal to 10−9 meters (that is, 10 to the power of -9, 0.000000001).

Answer 2

The diameter of a hydrogen atom in its ground state is approximately 5.3 x 10^-11 meters.

Answer 3

The diameter of a ground-state hydrogen atom in meters using scientific notation is 1.06×10−10.

Answer 4

This diameter (covalent) is approx. 50.10e-10 cm.

Answer 5

The covalent diameter is approx. 50.10e-3 nm.

Answer 6

0.00001 mm

Answer 7

I think is 10 g micro