Consider a HCN molecule at 25°C. Calculate the Doppler broadening (in Hz) if a rotational, vibrational, and an electronic transition occur at 10 cm⁻¹, 1500 cm⁻¹, and 60000 cm⁻¹, respectively.

Rotational transition Doppler broadening: For a rotational transition at 10 cm⁻¹, the Doppler broadening can be calculated using the formula Δν = ν₀ * (v/c) * √(2kT/m), where ν₀ is the transition frequency, v is the molecule's velocity, c is the speed of light, k is the Boltzmann constant, T is the temperature, and m is the molecule's mass. Plugging in the values for HCN at 25°C, we get a Doppler broadening of ~1.68 MHz.

Vibrational transition Doppler broadening: In a vibrational transition at 1500 cm⁻¹, the Doppler broadening depends on the reduced mass of the vibrating atoms and the vibrational amplitude. At 25°C, the Doppler broadening can be calculated to be ~252.03 GHz.

Electronic transition Doppler broadening: Electronic transitions at 60000 cm⁻¹ are influenced by the speed of the electrons and the energy difference between the electronic states. The Doppler broadening can be estimated to be ~10.08 THz at 25°C.

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