Introduction:
In solid-state physics, the energy gap between the valence band and the conduction band plays a crucial role in determining the electrical conductivity of a material. The population of conduction electrons is directly related to this energy gap. This question asks us to compare the concentration of conduction electrons in diamond and silicon at room temperature, given the energy gap values.

Given Information:
- Energy gap (delta E) for silicon = 1.1 eV
- Energy gap (delta E) for diamond = 6.0 eV
- Temperature (T) = 300 K
- The population of conduction electrons is roughly proportional to e^(-delta E/2kt)

Calculating the Ratio:
To find the ratio of the concentration of conduction electrons in diamond to that in silicon, we need to calculate the population of conduction electrons for both materials using the given formula.

Calculation for Silicon:
- delta E = 1.1 eV
- T = 300 K
- k = Boltzmann constant = 8.6173 × 10^(-5) eV/K (known constant)

Using the formula, the population of conduction electrons in silicon can be calculated as:
population_silicon = e^(-delta E/2kt)

Calculation for Diamond:
- delta E = 6.0 eV
- T = 300 K
- k = Boltzmann constant = 8.6173 × 10^(-5) eV/K (known constant)

Using the formula, the population of conduction electrons in diamond can be calculated as:
population_diamond = e^(-delta E/2kt)

Calculating the Ratio:
To find the ratio, we divide the population of conduction electrons in diamond by the population in silicon:
ratio = population_diamond / population_silicon

Explanation:
The ratio calculated above represents the concentration of conduction electrons in diamond compared to silicon at room temperature. A higher ratio indicates a higher concentration of conduction electrons in diamond compared to silicon.

The energy gap between the valence band and the conduction band determines the ease with which electrons can move from the valence band to the conduction band. A larger energy gap means fewer electrons can overcome this barrier and transition to the conduction band, resulting in a lower concentration of conduction electrons.

In this case, diamond has a significantly larger energy gap (6.0 eV) compared to silicon (1.1 eV). This means that diamond has a higher energy barrier for electrons to move to the conduction band, resulting in a lower concentration of conduction electrons compared to silicon.

Therefore, the ratio of the concentration of conduction electrons in diamond to that in silicon at room temperature will be less than 1, indicating that silicon has a higher concentration of conduction electrons compared to diamond.