Respuesta :
Answer:
The atomic radius of sodium is 185.59 pm.
Sodium metal will float in water.
Explanation:
a) To calculate the density of metal, we use the equation:
[tex]\rho=\frac{Z\times M}{N_{A}\times a^{3}}[/tex]
where,
[tex]\rho[/tex] = density = [tex]0.97 g/cm^3[/tex]
Z = number of atom in unit cell = 2 (BCC)
M = atomic mass of metal = 22.99 g/mol
[tex]N_{A}[/tex] = Avogadro's number = [tex]6.022\times 10^{23}[/tex]
a = edge length of unit cell = ?
Putting values in above equation, we get:
[tex]0.97 g/cm^3=\frac{2\times 22.99}{6.022\times 10^{23}\times (a)^3}[/tex]
[tex]a=4.286\times 10^{-8} cm=4.286\times 10^{-8}\times 10^{10} pm = 428.6 pm[/tex]
[tex]1 cm = 10^{10} pm[/tex]
To calculate the radius, we use the relation between the radius and edge length for BCC lattice:
[tex]R=\frac{\sqrt{3}a}{4}[/tex]
where,
R = radius of the lattice = ?
a = edge length = 428.6 pm
Putting values in above equation, we get:
[tex]R=\frac{\sqrt{3}\times 428.6}{4}=185.59 pm[/tex]
The atomic radius of sodium is 185.59 pm.
b)
Density of water = D = 1 g/mL = [tex]1 g/cm^3[/tex]
( [tex]1 mL = 1cm^3[/tex])
Density of the sodium metal = d =[tex]0.97 g/cm^3[/tex]
D > d ( float)
Since, the density of the sodium metal is less than the water's density which means that sodium metal will float in water.
A) The atomic radius of sodium is : 185.59 pm
B) The sodium metal will still float on water ( i.e. True )
Given data :
Atomic weight of Sodium metal = 22.99 g/cm³
Density of sodium metal = 0.97 g/cm³
Avogadro's number ( Na ) = 6.022 * 10²³
A) Determine the atomic radius of sodium
First step : Calculate the EDGE length of the sodium metal
P = [tex]\frac{Z*M}{N_{a}*A^{3} }[/tex]
where ; z = 2 BCC , M = 22.99 g/mol, Na = 6.022 * 10²³ , P = 0.97 g/cm³
Insert values into equation ( 1 ) above
∴ A = 428.6 pm
Next step : Determine the atomic radius of sodium metal
R = [tex]\frac{\sqrt{3A} }{4}[/tex] = [tex]\frac{\sqrt{3* 428.6} }{4}[/tex] = 185.59 pm
B) The sodium metal will still float on water because the density of sodium = 0.97 g/cm³ is less than the density of water 1 g/cm³.
Hence we can conclude that the atomic radius of sodium is : 185.59 pm and The sodium metal will still float on water ( i.e. True ).
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