A gas of $$hydrogen-like$$ ions is prepared in such a way that ions are only in the ground state and the first excited state. A monochromatic light of wavelength $$1218$$ Å is absorbed by the ions. The ions are lifted to higher excited states and emit radiation of six wavelength, some higher and some lower than the incident wavelength. Calculate the values of the minimum wavelengths (in$$ Å$$).

Question

A gas of $$hydrogen-like$$ ions is prepared in such a way that ions are only in the ground state and the first excited state. A monochromatic light of wavelength $$1218$$ Å is absorbed by the ions. The ions are lifted to higher excited states and emit radiation of six wavelength, some higher and some lower than the incident wavelength. Calculate the values of the minimum wavelengths (in$$ Å$$).

Infinity Learn · Accepted Answer

Incident photon energy $$E=124311218=10.2eVWhen$$ six wavelengths are emitted that means electrons are excited to n $$=$$ $$4$$ and by absorption of $$10.2$$ eV if electrons excite from $$n1$$ to $$n2$$ $$=$$ $$4$$ we $$use10.2=13.6Z21n12$$−$$116For$$ Z $$=$$ $$1$$ this is not possibleFor Z $$=$$ $$2$$ we get $$n1=2For$$ Z $$=$$ $$3$$ onward this is not PossibleThus Z $$=$$ $$2$$ and transition is from $$n1$$ $$=$$ $$2$$ to $$n2$$ : $$4Minimum$$ wavelength (maximum$$ $$energy) emission is fortransition $$4$$ → $$1$$⇒λ$$min=1243112.75$$×$$4=243.74$$Å≈$$244$$Å

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