At a place directly below a thundercloud, the induced electric charge on the surface of the Earth is +1.0 X 〖10〗^(-7) coulomb per square meter of surface. How many singly charged positive ions per square meter does this represent? The number of atoms on the surface of a solid is typically 2.0 X 〖10〗^19 per square meter. What fraction of these atoms must be ions to account for the above electric charge?

To calculate the number of singly charged positive ions per square meter, we need to divide the induced electric charge by the elementary charge (e).

The elementary charge (e) is the charge of a single electron or proton, which is approximately 1.6 x 10^(-19) coulombs.

So, the number of ions per square meter can be calculated as follows:

Number of ions = Induced electric charge / Elementary charge

Number of ions = (1.0 x 10^(-7) C/m^2) / (1.6 x 10^(-19) C)

To calculate the fraction of these ions compared to the total number of atoms on the surface, we need to know the ratio between the number of ions and the total number of atoms.

Total number of atoms per square meter = 2.0 x 10^(19) atoms/m^2

Fraction of atoms that must be ions = Number of ions / Total number of atoms

Fraction of atoms that must be ions = (Number of ions) / (2.0 x 10^(19) atoms/m^2)

Let's now calculate the values:

Number of ions = (1.0 x 10^(-7) C/m^2) / (1.6 x 10^(-19) C) ≈ 6.25 x 10^11 ions/m^2

Fraction of atoms that must be ions = (6.25 x 10^11 ions/m^2) / (2.0 x 10^19 atoms/m^2)

Now, we can simplify the fraction:

Fraction of atoms that must be ions ≈ 3.13 x 10^(-9) or 3.13 nanofraction

Therefore, the fraction of atoms that must be ions to account for the above electrical charge is approximately 3.13 x 10^(-9) or 3.13 nanofraction.