[Ilikebugs]

The covalent radius of hydrogen is 74 pm. Assume that hydrogen atoms could be arranged side-by-side in a single line. What is the mass of a line of hydrogen atoms that is exactly 10 cm long?

I got that the number of hydrogen atoms is equal to (10^13 pm)/(148 pm) and dividing by Avogadro's number gives 1.1*10^-13 moles which multiplying by 1g/mol is 1.1*10^-13 grams, but apparently the answer is 1.1*10^-15 g

[Borek]

Why 10¹³?

[Ilikebugs]

Oh I thought that 10cm was 10^13pm but it's actually 10^10, but that still gives an answer of 1.1*10^-16 instead.

[mjc123]

No, 1 m is 10¹² pm, so 10 cm is???

[Ilikebugs]

Oh if 10cm is 10^11 pm then that obtains the right answer.

[Enthalpy]

As a side note, the radius of an atom is very ill-defined. Atoms themselves are fuzzy, and the distance between the nuclei depends on what nuclei, what bond, and pretty much everything. If one really can't avoid using an atomic radius, then he should check exactly what definition is used for the data he finds. "Covalent" radius isn't accurate enough. 20% discrepancy is common.

This goes worse with hydrogen, whose single shell changes much its extension depending on the bonds. As an illustration, covalent water and polyethylene at room temperature pack 1.5× and 1.7× as many hydrogen atoms per volume unit as solid hydrogen at 20K 1atm does, despite oxygen and carbon taking some room too.