Terahertz to Hertz Converter
Common Conversions
| THz | Hz |
|---|---|
| 0.1 | 100000000000 |
| 0.5 | 500000000000 |
| 1 | 1000000000000 |
| 2 | 2000000000000 |
| 5 | 5000000000000 |
| 10 | 10000000000000 |
| 25 | 25000000000000 |
| 50 | 50000000000000 |
| 100 | 100000000000000 |
| 1000 | 1000000000000000 |
Why this conversion matters in chemistry
Mid-infrared vibrational spectroscopy hits this regularly. A 30 THz fingerprint band at 1000 cm⁻¹ converts to 3.0 × 10¹³ Hz — the frequency that corresponds to 124 meV per vibrational quantum on a Planck-relation calculation. The 10¹² Hz per THz is just the SI tera prefix written as one number. What this is, really: the step between THz time-domain spectrometer output (where photon-frequency is the natural axis) and the wavenumber form FTIR spectra and standard vibrational-mode tables use.
Formula
Where the factor comes from
The tera prefix supplies the 10¹² and the hertz supplies everything else. One hertz is one cycle per second, and the second is fixed by declaring the cesium-133 ground-state hyperfine transition to be exactly 9192631770 Hz — so the whole frequency scale hangs on a single microwave line, and a terahertz is that line's frequency multiplied by about 108.8. Neither half is measured; both are stipulated. What the symbol will not tell you is which reciprocal second is meant. The hertz is reserved for cycles of a periodic phenomenon; angular frequency in radians per second shares the dimensions but runs 2π larger; the becquerel is also s⁻¹ while counting decays that are not periodic at all. The prefix step is trivial, and keeping those three apart is the actual work.
Precision and significant figures
Since 10¹² is exact, significant figures are entirely a question of what the measurement handed you. In a time-domain experiment the frequency resolution follows from the length of the recorded waveform — a longer scan buys finer spacing — and quoting a band center to more digits than the window supports asserts something the data does not contain. Condensed-phase chemistry rarely needs many: intermolecular and lattice modes are broad, so two or three figures usually describe a THz band completely. Write 1.42 THz as 1.42 × 10¹² Hz and stop, because 1,420,000,000,000 Hz implies thirteen figures nobody measured. Frequency counting itself reaches far past any linewidth in a solid or a solution, so the sample is always the limit here, never the arithmetic.
Worked Examples
The conversion anchor — about the lower edge of the far-infrared region.
Mid-infrared — the fingerprint vibrational region.
Boundary between microwave and THz regions.
Common mistakes
Treating wavenumbers as a frequency
A band at 33.36 cm⁻¹ is not 33.36 of anything per second. Wavenumber is reciprocal wavelength, and crossing to frequency requires the speed of light: 1 THz corresponds to 33.356 cm⁻¹. Instrument software that plots one axis while reporting the other makes the slip easy, and the resulting factor near 3 × 10¹⁰ is obvious only if you stop to check the exponent.
Angular frequency hides a 2π
Relaxation models and lineshape fits are usually written in ω, and ω = 2πν. A 1 THz mode is 6.283 × 10¹² rad/s, not 10¹² rad/s. Both quantities are quoted in reciprocal seconds, so the units never catch the error, and a damping or rate constant fitted with the wrong one lands 6.28 times off in whichever direction the equation was arranged.
THz quanta sit near thermal energy
One terahertz is 4.136 meV, about 0.399 kJ/mol, and corresponds to 48 K on the h/k scale. At 298 K, RT is roughly 2.48 kJ/mol, so modes in this region carry appreciable excited-state population. Treating a THz band with the ground-state-only picture that serves well for a mid-infrared fundamental will misstate intensities and any vibrational partition-function term built from it.