The diameter of a neutral neon atom is about 1.4 multiplied by 102 pm. Suppose that we could line up neon atoms side by side in contact with one another. Approximately how many neon atoms would it take to make the distance from end to end 1 cm?

I got 2.4e-8, but it was wrong. What is the correct method for this?

And

What is the mass in grams of a single atom of each of the following elements?

Os

I got 3.16 x 10^24, but got it wrong. I just divided the atomic mass by Av. number.

Convert 1.4 x 10^2 pm to cm.

1.4 x 10^2 pm x (1 m/10^9 pm) x (100 cm/m) = ??
That number divided into 1 cm = ??

Os/6.022 x 10^23 is the correct way of doing it BUT you can't possible come out with a 10^24. 3.15 x 10^-22 maybe.
To be technical about it, 109.23 is the AVERAGE mass of all of the Os atoms found in nature. To find the mass of a single atom of Os one should give you the mass number of the isotope (184,189, 190, etc) of Os for which you are to calculate the mass.

To determine the number of neon atoms required to make a distance of 1 cm, you can use the concept of linear packing. In this scenario, the atoms are lined up side by side in contact with one another.

Given that the diameter of a neutral neon atom is about 1.4 x 10^2 pm, we can calculate the radius of the atom as half of the diameter, which is 7 x 10^1 pm.

To calculate the total distance covered by the neon atoms, we need to consider both the radius of a single atom and the space between the atoms. The space between the atoms can be calculated by subtracting the diameter of an atom from the total distance.

Therefore, the space between the neon atoms is 1 cm - 1.4 x 10^2 pm (which needs to be converted to cm) = 1 cm - 1.4 x 10^-10 cm ≈ 1 cm.

Since the space between the atoms is negligible compared to the total distance, the number of neon atoms required to make a distance of 1 cm is essentially the same as if they were lining up with no space in between. So, the number of neon atoms needed is given by:

Number of neon atoms = 1 cm / 1.4 x 10^2 pm = 1 cm / (1.4 x 10^-10 cm) = 7.14 x 10^7

Therefore, it would take approximately 7.14 x 10^7 neon atoms to make the distance from end to end 1 cm.

For the second question regarding the mass of a single atom of the element Os (osmium), you need to use the atomic mass of osmium and convert it into grams.

The atomic mass of Os is approximately 190.23 g/mol.
To calculate the mass of a single Os atom, divide the atomic mass by Avogadro's number (6.022 x 10^23 mol^-1). This will give you the mass in grams.

Mass of a single Os atom = (190.23 g/mol) / (6.022 x 10^23 mol^-1) ≈ 3.16 x 10^-22 g

So, the correct mass in grams of a single Os atom is approximately 3.16 x 10^-22 g, not 3.16 x 10^24 g. Avoid confusion and verify that you are correctly dividing the atomic mass by Avogadro's number to get the correct result.