Estimate the width of a spectral line in both frequency (ν, Hz) and wavenumbers (ν̃, cm^-1) orig

Question

Estimate the width of a spectral line in both frequency ($\nu$, Hz) and wavenumbers ($\tilde{\nu}$, cm$^{-1}$) originating from the decay of a state with a lifetime of 1 ns. (Note: $E = h\nu = \frac{hc}{\lambda} = hc\tilde{\nu}$)

          Estimate the width of a spectral line in both frequency ($\nu$, Hz) and wavenumbers ($\tilde{\nu}$, cm$^{-1}$) originating from the decay of a state with a lifetime of 1 ns.
(Note: $E = h\nu = \frac{hc}{\lambda} = hc\tilde{\nu}$)

Estimate the width of a spectral line in both frequency (ν, Hz) and wavenumbers (ν̃, cm^-1) originating from the decay of a state with a lifetime of 1 ns.
(Note: E = hν = (hc)/(λ) = hcν̃)

Added by Denise R.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Adi S

06/12/2023

Step 1

Step 1: The uncertainty principle states that the product of the uncertainty in energy (ΔE) and the uncertainty in time (Δt) is greater than or equal to Planck's constant divided by 4π: $$ΔEΔt ≥ \frac{h}{4π}$$ Show more…

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Estimate the width of a spectral line in both frequency (v, Hz) and wavenumbers (v, cm¯¹) originating from the decay of a state with a lifetime of 1 ns. (Note: E = hv=hc/x = hcv)