Platinum is a highly conductive metal, but it is not as good a conductor as silver or copper. The electrical conductivity of platinum is determined by its atomic structure, impurities, and temperature. While platinum has a single valence electron and is in the same column as gold and silver in the periodic table, its larger atomic radius and face-centered cubic (fcc) crystal structure make it less efficient at conducting electricity compared to the hexagonal close-packed (hcp) structure of silver and the fcc structure of gold.

## Electrical Conductivity of Platinum

The electrical conductivity of a material is determined by the number of valence electrons in its atoms and the strength of the metallic bonding between the atoms. In a metallic bond, the atoms are surrounded by a “sea of electrons” that are free to move and conduct electricity. The strength of the metallic bonding depends on the size of the atoms and the number of valence electrons.

Platinum has a larger atomic radius than silver and gold, which means that the valence electrons are farther away from the nucleus and are less tightly bound. This should make platinum a better conductor, but the opposite is true. The reason for this is not fully understood, but it is thought to be due to the crystal structure of platinum.

Platinum has a face-centered cubic (fcc) crystal structure, which is less efficient at conducting electricity than the hexagonal close-packed (hcp) structure of silver and the face-centered cubic (fcc) structure of gold. The fcc structure of platinum has a lower electron mobility, which reduces its electrical conductivity.

## Factors Affecting Electrical Conductivity of Platinum

The electrical conductivity of platinum is also affected by impurities and temperature. Adding impurities to platinum decreases its conductivity, as the impurities disrupt the flow of electrons and create scattering centers. Increasing the temperature also decreases the electrical conductivity of platinum due to thermal excitation of the atoms, which increases the scattering of electrons.

The relationship between temperature and conductivity is linear, but it breaks down at low temperatures. At low temperatures, the electrical conductivity of platinum can increase due to the reduction in electron scattering.

## Wiedemann-Franz Law

The theorem related to the conductivity of metals is called the Wiedemann-Franz law. It states that the electrical conductivity of a metal is proportional to its thermal conductivity divided by its temperature. This law is used to calculate the electrical conductivity of a metal based on its thermal conductivity and temperature.

The formula for electrical conductivity is:

$\sigma = \frac{1}{\rho}$

where $\sigma$ is the electrical conductivity and $\rho$ is the electrical resistivity.

## Examples of Electrical Conductivity of Metals

Here are some examples of the electrical conductivity of various metals at room temperature:

Metal | Electrical Conductivity (S/m) |
---|---|

Silver | $6.3 \times 10^7$ |

Copper | $5.96 \times 10^7$ |

Gold | $4.5 \times 10^7$ |

Platinum | $9.43 \times 10^5$ |

As you can see, platinum has a lower electrical conductivity compared to silver, copper, and gold.

## Numerical Problems

Here are some numerical problems related to the electrical conductivity of metals:

- A copper wire has a resistance of 0.5 Ω and a cross-sectional area of 1 mm². What is its electrical conductivity?

Solution: The electrical conductivity of copper is $5.96 \times 10^7$ S/m. The resistance of a conductor is given by the formula $R = \rho \frac{\ell}{A}$, where $\ell$ is the length of the conductor, $A$ is the cross-sectional area, and $\rho$ is the electrical resistivity. Rearranging this formula to solve for $\rho$ gives $\rho = \frac{R A}{\ell}$. Substituting the given values into this formula gives $\rho = \frac{0.5 \times 10^{-6} \times 1}{1000} = 5 \times 10^{-8}$ Ω·m. The electrical conductivity is the reciprocal of the electrical resistivity, so $\sigma = \frac{1}{5 \times 10^{-8}} = 2 \times 10^7$ S/m.

- A platinum wire has a resistance of 10 Ω and a length of 1 m. What is its cross-sectional area?

Solution: The electrical conductivity of platinum is $9.43 \times 10^5$ S/m. The resistance of a conductor is given by the formula $R = \rho \frac{\ell}{A}$, where $\ell$ is the length of the conductor, $A$ is the cross-sectional area, and $\rho$ is the electrical resistivity. Rearranging this formula to solve for $A$ gives $A = \frac{\rho \ell}{R}$. Substituting the given values into this formula gives $A = \frac{9.43 \times 10^{-6} \times 1}{10} = 9.43 \times 10^{-7}$ m².

## Figures and Data Points

Here are some figures and data points related to the electrical conductivity of metals:

Figure 1 shows the electrical conductivity of various metals as a function of temperature.

Figure 2 shows the electrical conductivity of copper as a function of frequency.

Figure 3 shows the electrical conductivity of aluminum as a function of impurity concentration.

Data Points:

– Silver: $6.3 \times 10^7$ S/m at 20°C

– Copper: $5.96 \times 10^7$ S/m at 20°C

– Gold: $4.5 \times 10^7$ S/m at 20°C

– Platinum: $9.43 \times 10^5$ S/m at 20°C

## Values and Measurements

Here are some values and measurements related to the electrical conductivity of metals:

Values:

– The electrical conductivity of silver is $6.3 \times 10^7$ S/m.

– The electrical conductivity of copper is $5.96 \times 10^7$ S/m.

– The electrical conductivity of gold is $4.5 \times 10^7$ S/m.

– The electrical conductivity of platinum is $9.43 \times 10^5$ S/m.

Measurements:

– The electrical conductivity of a material is measured in siemens per meter (S/m).

– The electrical resistivity of a material is measured in ohm-meters (Ω·m).

– The cross-sectional area of a conductor is measured in square meters (m²).

– The length of a conductor is measured in meters (m).

## Other Quantifiable Details

Here are some other quantifiable details related to the electrical conductivity of metals:

- The electrical conductivity of a material depends on its temperature, frequency, and impurity concentration.
- The electrical conductivity of a material is inversely proportional to its electrical resistivity.
- The electrical conductivity of a material is proportional to its cross-sectional area and inversely proportional to its length.
- The electrical conductivity of a material is a measure of its ability to conduct electric current.

References:

– Electrical Conductivity of Metals

– Platinum Catalysts and Electrical Conductivity

– Comparison of Silver and Platinum Conductivity

– Best Metals for Electrical Conductivity

– Electrical Conductance

Hi, I’m Akshita Mapari. I have done M.Sc. in Physics. I have worked on projects like Numerical modeling of winds and waves during cyclone, Physics of toys and mechanized thrill machines in amusement park based on Classical Mechanics. I have pursued a course on Arduino and have accomplished some mini projects on Arduino UNO. I always like to explore new zones in the field of science. I personally believe that learning is more enthusiastic when learnt with creativity. Apart from this, I like to read, travel, strumming on guitar, identifying rocks and strata, photography and playing chess.