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Exercise:
Calculate the shortest wavelength in the spectrum of a hydrogen atom for an electron transitioning to abcliste abc the ground state. abc the third excited state n. abcliste

Solution:
abcliste abc The shortest wavelength corresponds to the highest frequency and therefore the highest photon energy. This is just the ionisation energy of the hydrogen atom i.e. the negative energy of the groundstate: E_gamma -E_ frachcssclambdamin Solving for the wavelength yields ssclambdamin laaF -frachcEgr resultlaaP- quad textrmUV abc The photon energy for electrons transitioning from an energy level E_m m to the third excited state E_ is E_gamma E_m - E_ E_leftfracm^-frac^right E_leftfracm^-fracright The maximum energy corresponds to the limit for mtoinfty: sscEgammamax lim_mtoinfty E_leftfracm^-fracright -fracE_ frachclambda It follows for the wavelength lambda labF -fractimeshcEgr resultlabP- quad textrminfrared abcliste
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Exercise:
Calculate the shortest wavelength in the spectrum of a hydrogen atom for an electron transitioning to abcliste abc the ground state. abc the third excited state n. abcliste

Solution:
abcliste abc The shortest wavelength corresponds to the highest frequency and therefore the highest photon energy. This is just the ionisation energy of the hydrogen atom i.e. the negative energy of the groundstate: E_gamma -E_ frachcssclambdamin Solving for the wavelength yields ssclambdamin laaF -frachcEgr resultlaaP- quad textrmUV abc The photon energy for electrons transitioning from an energy level E_m m to the third excited state E_ is E_gamma E_m - E_ E_leftfracm^-frac^right E_leftfracm^-fracright The maximum energy corresponds to the limit for mtoinfty: sscEgammamax lim_mtoinfty E_leftfracm^-fracright -fracE_ frachclambda It follows for the wavelength lambda labF -fractimeshcEgr resultlabP- quad textrminfrared abcliste
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quantum physics
Tags
energy level, hydrogen atom, photon
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ENG (English)
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Calculative / Quantity
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