JEE Main 2019 · Physics · Atoms, Nuclei and Dual Nature of Radiation · easy

A Li^2+ ion has a single electron. The wavelength of the photon emitted when this electron makes a transition from the third orbit to the second…

Single correct option

\mathrm{Li^{2+}}

ion has a single electron. The wavelength of the photon emitted when this electron makes a transition from the third orbit to the second orbit is nearly (take the ground state energy of hydrogen as

-13.6\ \mathrm{eV}

and

hc=1240\ \mathrm{eV\,nm}

)

A. $164\ \mathrm{nm}$
B. $73\ \mathrm{nm}$
C. $656\ \mathrm{nm}$
D. $36\ \mathrm{nm}$

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Answer: (B) $73\ \mathrm{nm}$

For a hydrogen-like ion

E_n=-13.6\,Z^2/n^2\ \mathrm{eV}

with

Z=3

. The photon energy is

\Delta E=13.6\times9\left(\dfrac14-\dfrac19\right)=13.6\times9\times\dfrac5{36}=17.0\ \mathrm{eV}

. Then

\lambda=\dfrac{1240}{17.0}\approx73\ \mathrm{nm}

, which lies in the extreme ultraviolet. Using

Z=1

gives the hydrogen H-alpha line near

656\ \mathrm{nm}

and

Z=2

gives

164\ \mathrm{nm}

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