Mercury is the only chemical metal that is a liquid at room temperature. Discove
ID: 531728 • Letter: M
Question
Mercury is the only chemical metal that is a liquid at room temperature. Discovered about 3500 years ago, it has had a wide range of uses from chemical devices, and mineral processing applications laboratory devices, and even medicine. As its high toxicity has come to be understood, its use has greatly declined in recent years. a) Mercury is a bivalent metal. Use the information provided to calculate the electron number density. b) Calculate the Fermi energy for mercury. c) Calculate the Fermi speed. v = Squareroot 2 E_p/m_e.Explanation / Answer
a) Calculate the number density of Hg
n = z NA/VA
Where z = 2
NA is the Avogadro’s constant= 6.023 × 10^23 atoms/mol
VA is the molar volume.
To calculate the molar volume (VA)
VA=M /
Where,
M = 200.59 g/mol
is the density = 13.534 g/cm^3
Va = 200.59 g/mol/13.534 = 14.821 cm^3/mol = 1.48 x 10^-5m^3/mol
Now calculate electron density by using equation
n = z NA/VA
n = 2 x 6.023 × 10^23atoms/mol/1.48 x 10^-5m^3/mol
n = 8.139 x 10^28atoms/ m^3
n = 8.14 x 10^28 atoms/ m^3
b)The Fermi Energy can be calculated by the following equation:
EF = ^2/8Mc (3n/ )^2/3
Where,
EF = Fermi Energy;
Mc= mass of the fermions;
= Planck’s constant;
n = electron number density
EF = (6.625 × 10^34)^2/8(9.11 × 1031) (3(8.14 × 10^28/3.14)^2/3
= 7 .1ev
c) Calculate the Fermi speed –
V = C (2EF/mc^2)^1/2
V = 3x 10^8 m/s (2 x 7.1ev/511000ev)^1/2
V = 3 x 10^8 m/s x 5.26 x 10^-3
V = 1.58 x 10^6 m/s