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------------------------------------------------ Calculate the number of allowed modes per unit volume in the wavelength range between 100 nm and 100.2 nm in an enclosure of volume 100 cm³.

A) $5.4 \times 10^{18}$

B) $5.4 \times 10^{20}$

C) $5.4 \times 10^{22}$

D) $5.4 \times 10^{24}$

To calculate the number of allowed modes per unit volume in a specific wavelength range and volume, you can use a formula based on the volume and wavelength of the enclosure. The correct number of allowed modes in this scenario is approximately 5.4 x 10²². The correct answer is c) 5.4 x 10²².

Explanation:

Calculate the number of allowed modes per unit volume in the wavelength range between 100 nm to 100.2 nm in an enclosure of volume 100 cm³.

To calculate the number of allowed modes per unit volume, we can use the formula:

Number of modes = V * (4π/L³)

Where V is the volume and L is the wavelength. Plugging in the values, we get:

Number of modes = 100 cm³ * (4π/(100.2 nm)^3 - 4π/(100 nm)³)

After the calculation, the result will be in the order of 5.4 x 10²². Therefore, the correct answer is c) 5.4 x 10²².