Answer:
Density of the He atom = 12.69 g/cm³
Explanation:
From the information given:
Since 1 mole of an atom = 6.022x 10²³ atoms)
1 atom of He = [tex]1 \ atom \times (\dfrac{1 \ mole}{ 6.022 \times 10^{23} \ atoms}) \times ( \dfrac{4.003 \ grams}{ 1 \ mole})[/tex]
[tex]=6.647 \times 10^{-24} \ grams[/tex]
The volume can be determined as folows:
since the diameter of the He atom is approximately 0.10 nm
the radius of the He = [tex]\dfrac{0.10}{2}[/tex] = 0.05 nm
Converting it into cm, we have:
[tex]0.05 nm \times \dfrac{10^{-9} \ meters}{ 1 nm} \times \dfrac{ 1 cm }{10^{-2} \ meters}[/tex]
[tex]=5 \times 10^{-9} \ cm[/tex]
Assuming that it is a sphere, the volume of a sphere is
= [tex]\dfrac{4}{3}\pi r^3[/tex]
= [tex]\dfrac{4}{3}\pi \times (5\times 10^{-9})^3[/tex]
= [tex]5.236 \times 10^{-25} \ cm^3[/tex]
Finally, the density can be calcuated by using the formula :
[tex]Density = \dfrac{mass}{volume}[/tex]
[tex]D = \dfrac{6.647 \times 10^{-24} \ grams }{ 5.236 \times 10^{-25} \ cm^3}[/tex]
D = 12.69 g/cm³
Density of the He atom = 12.69 g/cm³
Answer:
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
