Question

. Assume that the nucleus of fluorine atom is a sphere with a radius of 5 x 10 cm.
Calculate the density of matter in the fluorine nucleus. (F = 19)​

Answer 1

Answer:

The density of an atom of flourine with a radius of 5 × 10 cm is 0.09071 amu/cm³ .

Explanation:

Density is given by the following formula:

        Mass / volume

Calculate the volume of the flourine atom:

Formula for Volume of a sphere:  4πr³/3

The radius of this atom is 5 × 10 cm = 50 cm

Volume  = (4 × 3.142 × 50) / 3

             = 209.47 cm³

The mass of atomic mass of the flourine atom is 19 amu

Therefore we can use the formula denisty = mass/volume to get the density of the matter in the flourine nucleus ( the mass of an atom is concentrated in the nuceus, the surrounding electrons are of neglibible weight)

Density = mass/volume

            = 19 amu / 209.47 cm³

            = 0.09071 amu/cm³

Therefore the density of this flourine nucleus is 0.09071 amu/cm³

Answer 2

Explanation:

Explanation:

We can calculate the molecules in 500 cm³ of hydrogen gas using ideal gas law and Avogadro's constant.

Ideal gas law: 1 mole of any ideal gas occupies exactly 22.4 liters by volume at STP

Avogadro's constant: 1 mole of any substance contains exactly 6.022 × 10²³ molecules.

Moles of hydrogen in 500 cm³ of hydrogen

22.4 liters = 22400 cm³

If 22400 cm³ = 1 mole

Then 500cm³ = 1 mole × 500cm³/22400cm³

                      ≈ 0.02232 moles

We can apply Avogadro's number/constant to calculate the number of molecules in the 0.02232 molecules of hydrogen gas.

If 1 mole = 6.022 × 10²³ molecules

Then 0.02232 moles = 6.022 × 10²³ × 0.02232 moles/1 mole

                                = 1.3441104 ×10²³ molecules

Therefore there are 1.3441104 ×10²³ molecules of hydrogen in 500cm³ of hydrogen gas. ( which has been given as n)

Find the number of molecules in 25 cm³ of oxygen at STP using the same formula.

22400 cm³ = 1 mole

25 cm³ = 1 mole × 25 cm³/22400 cm³

            ≈ 0.00112 moles

Find number of molecules in 0.00112 moles of oxygen

If 1 mole = 6.022 × 10²³ molecules

Then 0.00112 moles = 6.022 × 10²³ × 0.00112 moles/1 mole

                                = 6.721 × 10²⁰ molecules

Therefore there are 6.721 × 10²⁰ molecules of oxygen in 25cm³ of oxygen gas.

You can express this number in terms of n in respect to the number of molecules of hydrogen:

If  1.3441104 ×10²³ = n

Then 6.721 × 10²³ = n × 6.721 × 10²⁰ / 1.3441104 ×10²³

                            = 5n

Therefore in terms of n, there are 5n molecules of oxygen in 25cm³ of oxygen.