**Calculating the Volume of a Hydrogen Atom**

To determine the atomic weight of hydrogen, we need to calculate the volume of a hydrogen atom first. Since the hydrogen atom is assumed to be spherical, we can use the formula for the volume of a sphere:

V = (4/3) * π * r^3

Given that the radius of the hydrogen atom is 0.53 Å (angstroms), we can substitute this value into the formula to find the volume:

V = (4/3) * 3.14 * (0.53 Å)^3

**Converting Angstroms to Milliliters**

However, the density of the hydrogen atom is given in grams per milliliter. So, we need to convert the volume from angstroms to milliliters. The conversion factor between angstroms and milliliters is:

1 Å = 1 x 10^-24 ml

Converting the volume from Å^3 to ml:

V = (4/3) * 3.14 * (0.53 Å)^3 * 1 x 10^-24 ml/Å^3

**Calculating the Atomic Weight of Hydrogen**

Next, we need to determine the mass of hydrogen in grams. The density of hydrogen is given as 2.675 g/ml. We can use the formula:

Mass = Density * Volume

Substitute the density and the volume into the formula:

Mass = 2.675 g/ml * [(4/3) * 3.14 * (0.53 Å)^3 * 1 x 10^-24 ml/Å^3]

Simplifying the equation:

Mass = 2.675 g/ml * [(4/3) * 3.14 * (0.53)^3 * 1 x 10^-24]

Now, we can solve for the mass:

Mass = 2.675 * (4/3) * 3.14 * (0.53)^3 * 1 x 10^-24 g

Finally, we have the mass of hydrogen in grams. To calculate the atomic weight, we need to convert this mass from grams to atomic mass units (AMU). The conversion factor is:

1 g = 6.022 x 10^23 AMU

Using the conversion factor:

Atomic Weight = Mass * (6.022 x 10^23 AMU/g)

Substituting the mass into the equation:

Atomic Weight = 2.675 * (4/3) * 3.14 * (0.53)^3 * 1 x 10^-24 * (6.022 x 10^23 AMU/g)

Simplifying the equation:

Atomic Weight = 2.675 * (4/3) * 3.14 * (0.53)^3 * 1 x 10^-24 * 6.022 x 10^23 AMU

Finally, calculate the atomic weight using a calculator or by performing the arithmetic operations.