Question

The diameter of the He He atom is approximately 0.10 nm nm . Calculate the density of the He atom in g/cm 3 g/cm3 (assuming that it is a sphere).

Answer 1

12.7g/cm³

Step-by-step explanation:

Density is defined as the ratio of mass per unit volume of a substance.

Density = Mass/Volume

Since the shape of the Helium atom is a sphere, we will use the formula for calculating the volume of a sphere to get the volume of helium

Volume of a sphere = 4/3πr³ where r is the radius of the sphere.

Given the diameter of the sphere = 0.10nm

radius of the sphere = 0.10/2 = 0.05nm = 5*10⁻⁹cm

Volume of the sphere = 4/3 * 3.14 * (5*10⁻⁹)³

V = 4/3 * 3.14 * 125*10⁻²⁷

V = 1,570*10⁻²⁷/3

V = 523.33*10⁻²⁷

V = 5.233*10⁻²⁵cm³

Mass of the Helium atom = 6.6464731 × 10⁻²⁴ g

Density of the Helium atom in g/cm³ = 6.6464731 × 10⁻²⁴ g/5.233*10⁻²⁵cm³

Density of the Helium atom in g/cm³ = 1.27 * 10⁻²⁴⁻⁽⁻²⁵⁾g/cm³

Density of the Helium atom in g/cm³ = 1.27 * 10⁻²⁴⁺²⁵g/cm³

Density of the Helium atom in g/cm³ = 1.27 * 10¹g/cm³

Density of the Helium atom in g/cm³ = 12.7g/cm³

Hence the density of the He atom in g/cm³ is 12.7g/cm³

Answer 2

Density of the He atom = 12.69 g/cm³

Step-by-step explanation:

From the information given:

Since 1 mole of an atom = 6.022x 10²³ atoms)

1 atom of He =
`1 \ atom * ((1 \ mole)/( 6.022 * 10^(23) \ atoms)) * ( (4.003 \ grams)/( 1 \ mole))`

`=6.647 * 10^(-24) \ grams`

The volume can be determined as folows:

since the diameter of the He atom is approximately 0.10 nm

the radius of the He =
`(0.10)/(2)` = 0.05 nm

Converting it into cm, we have:

`0.05 nm * (10^(-9) \ meters)/( 1 nm) * ( 1 cm )/(10^(-2) \ meters)`

`=5 * 10^(-9) \ cm`

Assuming that it is a sphere, the volume of a sphere is

=
`(4)/(3)\pi r^3`

=
`(4)/(3)\pi * (5* 10^(-9))^3`

=
`5.236 * 10^(-25) \ cm^3`

Finally, the density can be calcuated by using the formula :

`Density = (mass)/(volume)`

`D = (6.647 * 10^(-24) \ grams )/( 5.236 * 10^(-25) \ cm^3)`

D = 12.69 g/cm³

Density of the He atom = 12.69 g/cm³