determine the wavelength for a transition from the v=0 to the v=1 level. Is this transition in the IR region of the electromagnetic spectrum?
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The vibrational energy in the harmonic oscillator picture is given by
E = hν₀( v + 1/2) , here v₀ is the threshold frequency and v is the transition level .
Now, energy of photon for a transition from 0 to 1 level is ∆E = E₁ - E₀
= hv₀(1 + 1/2) - hv₀(0 + 1/2)
= hv₀
We know, energy if photon is given by E = hv
so, hv = hv₀ ⇒v = v₀
hence, c/λ = v₀
λ = c/v₀
Here v₀ = 8.9626 × 10¹³ Hz [ given infrared region ]
so, λ = 3 × 10⁸/8.9626 × 10¹³ = 3345nm
Hence wavelength is 3345 nm
E = hν₀( v + 1/2) , here v₀ is the threshold frequency and v is the transition level .
Now, energy of photon for a transition from 0 to 1 level is ∆E = E₁ - E₀
= hv₀(1 + 1/2) - hv₀(0 + 1/2)
= hv₀
We know, energy if photon is given by E = hv
so, hv = hv₀ ⇒v = v₀
hence, c/λ = v₀
λ = c/v₀
Here v₀ = 8.9626 × 10¹³ Hz [ given infrared region ]
so, λ = 3 × 10⁸/8.9626 × 10¹³ = 3345nm
Hence wavelength is 3345 nm
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