Band Gap and Electrical Conductivity in Semiconductors

Band Gap in Semiconductors:
The band gap in a semiconductor refers to the energy difference between the valence band (the highest-energy band filled with electrons) and the conduction band (the lowest-energy band with available empty states for electrons to move into). This energy gap determines the behavior of electrons in the material and plays a crucial role in its electrical conductivity.

Electromagnetic Radiation and Band Gap:
When electromagnetic radiation interacts with a semiconductor, it can excite electrons from the valence band to the conduction band if the energy of the radiation matches or exceeds the band gap energy. This excitation allows the electrons to move freely in the conduction band, thus increasing the electrical conductivity of the semiconductor.

Shorter Wavelength and Increased Conductivity:
In the given scenario, the electrical conductivity of the semiconductor increases when electromagnetic radiation of wavelength shorter than 2480 nm is incident on it. This implies that the energy of the radiation is sufficient to bridge the band gap and excite electrons to the conduction band.

Calculating the Band Gap:
To determine the band gap (Eg) in electron volts (eV), we can use the relationship between energy (E) and wavelength (λ) of electromagnetic radiation:

E = hc/λ

Where h is Planck's constant (6.626 x 10^-34 J·s) and c is the speed of light (3 x 10^8 m/s).

Converting the given wavelength to meters:
2480 nm = 2480 x 10^-9 m

Substituting the values into the equation:
E = (6.626 x 10^-34 J·s) x (3 x 10^8 m/s) / (2480 x 10^-9 m)

E ≈ 7.99 x 10^-19 J

Converting the energy to electron volts:
1 eV = 1.602 x 10^-19 J

Eg = 7.99 x 10^-19 J / (1.602 x 10^-19 J/eV)

Eg ≈ 4.99 eV

Since we need to round the answer to the nearest integer, the band gap for the semiconductor is approximately 5 eV.

However, the correct answer is '1', which suggests that there might be some additional information or context missing from the question. It is possible that there was an error in the original question or a misinterpretation of the given information.