Question

A typical simple infrared spectrophotometer covers a wavelength range from 7 to 13 μm. Express its range in:
a) wavenumbers
b) hertz

Answer 1

Given info : A typical simple infrared spectrometer covers a wavelength range from 7 to 13μm.

To express : its range in

• (a) wavenumbers
• (b) Hertz (frequency)

solution : wavelength is reciprocal of wavelength.

when wavelength = 7μm

wavenumber = 1/wavelength = 1/7μm = 10⁶/7 m¯¹

≈ 142857 m¯¹

when wavelength = 13μ

wavenumber = 1/wavelength = 1/13μ = 10⁶/13 m¯¹

= 76923 m¯¹

Therefore the range of wavenumbers is 76923 to 142857 m¯¹.

frequency = speed of light/wavelength

when wavelength = 7μm

so, frequency = 3 × 10^8m/s/7μm ≈ 4.3 × 10¹³ Hz

when wavelength = 13μm

so frequency = 3 × 10^8m/s/13μm = 2.3 × 10¹³ Hz

Therefore the range of Frequencies is 2.3 × 10¹³ to 4.3 × 10¹³ Hz.