a typical simple Infrared spectrophotometer which covers a wavelength range from 3 to 15um. Express it's range in
(1). Wave number
(2). Hertz
(1) (1E-2 m / 3E-6 m) to (1E-2 m / 1.5E-5 m)
(2) (3E8 m / 3E-6 m) to (3E8 m / 1.5E-5 m)
To express the wavelength range of a typical simple Infrared (IR) spectrophotometer in wave number and Hertz, we first need to understand the relationship between these units.
1. Wave number:
Wave number is a unit used to express the number of waves per unit distance. It is denoted by the symbol cm⁻¹ (inverse centimeters). The wave number can be calculated using the formula:
Wave number (cm⁻¹) = 1 / wavelength (μm)
To express the IR spectrophotometer's wavelength range from 3 to 15 μm in wave number, we can use the above formula for the minimum and maximum wavelength:
Wave number (cm⁻¹) = 1 / 3 μm = 0.333 cm⁻¹ (minimum wave number)
Wave number (cm⁻¹) = 1 / 15 μm = 0.067 cm⁻¹ (maximum wave number)
Therefore, the range of the IR spectrophotometer in wave number is approximately 0.333 to 0.067 cm⁻¹.
2. Hertz:
Hertz (Hz) is the unit used to measure frequency, which represents the number of oscillations or cycles per second. To convert the wavelength range in micrometers to Hertz, we can use the following equation:
Frequency (Hz) = Speed of light (m/s) / Wavelength (m)
The speed of light is approximately 3 x 10^8 m/s.
For the minimum and maximum wavelength of the IR spectrophotometer (3 to 15 μm), we can calculate the frequency using the above formula:
Frequency (Hz) = (3 x 10^8 m/s) / (3 x 10^-6 m) = 1 x 10^14 Hz (minimum frequency)
Frequency (Hz) = (3 x 10^8 m/s) / (15 x 10^-6 m) = 2 x 10^13 Hz (maximum frequency)
Hence, the range of the IR spectrophotometer in Hertz is approximately 2 x 10^13 to 1 x 10^14 Hz.