Frequency of yellow light:
To calculate the frequency of the yellow light emitted from a sodium lamp, we can use the formula:

Frequency (f) = Speed of light (c) / Wavelength (λ)

The speed of light in a vacuum is a constant value of 3 x 10^8 meters per second (m/s). The wavelength of the yellow light is given as 580 nm (nanometers), which needs to be converted to meters by dividing by 10^9:

Wavelength (λ) = 580 nm / 10^9 = 5.8 x 10^-7 meters

Now we can substitute the values into the formula:

Frequency (f) = 3 x 10^8 m/s / 5.8 x 10^-7 meters

To simplify the calculation, we can divide the numerator and denominator by 10^8:

Frequency (f) = (3 / 5.8) x 10^8 / (10^-7)

The exponential form of 10^8 is 100,000,000, and the exponential form of 10^-7 is 0.0000001:

Frequency (f) = (3 / 5.8) x 100,000,000 / 0.0000001

Now we can perform the division:

Frequency (f) = 51,724,137,931,034,482,758.62 Hz

Therefore, the frequency of the yellow light emitted from the sodium lamp is approximately 51.7 x 10^18 Hz.

Wave number of yellow light:
The wave number (k) is a measure of the number of wavelengths per unit distance. It is defined as the reciprocal of the wavelength:

Wave number (k) = 1 / Wavelength (λ)

Using the previously calculated wavelength of 5.8 x 10^-7 meters:

Wave number (k) = 1 / 5.8 x 10^-7 meters

To simplify the calculation, we can multiply the numerator and denominator by 10^7:

Wave number (k) = (10^7) / (5.8 x 10^7) meters^-1

The exponential form of 10^7 is 10,000,000, and the exponential form of 10^7 is 0.000000058:

Wave number (k) = 10,000,000 / 0.000000058 meters^-1

Now we can perform the division:

Wave number (k) = 172,413,793,103,448,275.86 m^-1

Therefore, the wave number of the yellow light emitted from the sodium lamp is approximately 172.4 x 10^15 m^-1.