The ionization energy of a $$hydrogen-like$$ Bohr atom is $$4$$ Rdybergs. Find the wavelength of radiation emitted when the electron jumps from the first excited state to the ground state:[$$1Rydberg$$ $$=2.2$$×$$10$$−$$18joule$$][$$h=6.6$$×$$10$$−$$34Js$$,$$c=3$$×$$108m/s$$.]Bohr radius of hydrogen atom $$=5$$×$$10$$−$$11m$$]

Question

The ionization energy of a $$hydrogen-like$$ Bohr atom is $$4$$ Rdybergs. Find the wavelength of radiation emitted when the electron jumps from the first excited state to the ground state:[$$1Rydberg$$ $$=2.2$$×$$10$$−$$18joule$$][$$h=6.6$$×$$10$$−$$34Js$$,$$c=3$$×$$108m/s$$.]Bohr radius of hydrogen atom $$=5$$×$$10$$−$$11m$$]

Infinity Learn · Accepted Answer

The energy in the ground $$stateE1=$$−$$4$$ $$RydbergE1=$$−$$4$$×$$2.2$$×$$1018JThe$$ energy of the first excited state $$(n=2)E2=E14=-2.2$$×$$10$$−$$18JThe$$ energy differenceΔ$$E=E2$$−$$E1=3$$×$$2.2$$×$$10$$−$$18JNow$$, the wavelength of radiation emitted isλ$$=hc$$ΔEλ$$=6.6$$×$$10$$−$$34$$×$$3$$×$$1083$$×$$2.2$$×$$10$$−$$18=300A$$    ∘

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The ionization energy of a hydrogen-like Bohr atom is 4 Rdybergs. Find the wavelength of radiation emitted when the electron jumps from the first excited state to the ground state:[1Rydberg =2.2×10−18joule][h=6.6×10−34Js,c=3×108m/s.]Bohr radius of hydrogen atom =5×10−11m]

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