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.

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) \(5.4 \times 10^{24}\)

Answer :

Other Questions

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) \(5.4 \times 10^{24}\)