The band gap at 300 K of diamond cubic crystals of C, Si, Ge and Sn is 5.5, 1.2, 0.65 and 0.1 eV respectively. Identify the crystal which will have the highest electrical conductivity at 300K?a)Geb)Snc)Cd)SiCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Highest Electrical Conductivity at 300K

To determine the crystal with the highest electrical conductivity at 300K, we need to analyze the band gaps of diamond cubic crystals of C, Si, Ge, and Sn.

1. Band Gap:
The band gap is the energy difference between the valence band and the conduction band in a material. It determines the ability of a material to conduct electricity. A smaller band gap allows electrons to move more easily from the valence band to the conduction band, resulting in higher electrical conductivity.

2. Band Gap Values:
a) Diamond (C): The band gap of diamond is 5.5 eV.
b) Silicon (Si): The band gap of silicon is 1.2 eV.
c) Germanium (Ge): The band gap of germanium is 0.65 eV.
d) Tin (Sn): The band gap of tin is 0.1 eV.

3. Comparison and Analysis:
As we can see, the band gap decreases from diamond (C) to silicon (Si), germanium (Ge), and tin (Sn). This indicates that the electrical conductivity increases as the band gap decreases.

4. Explanation:
The crystal with the highest electrical conductivity at 300K is tin (Sn) because it has the smallest band gap of all the materials listed. With a band gap of only 0.1 eV, tin allows electrons to move more easily from the valence band to the conduction band, making it an excellent conductor of electricity at room temperature.

5. Conclusion:
In summary, tin (Sn) has the highest electrical conductivity at 300K among the given diamond cubic crystals. This is due to its small band gap of 0.1 eV, allowing for efficient movement of electrons and facilitating the flow of electric current through the material.

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