Atomic spectra

Chemistry Level 2

What would be the wavelength of the radiation emitted from an $\text{Li}^{2+}$ if the transition occurred from $n=3$ to $n=2?$

Hint: The transition from $n=3$ to $n=2$ in a neutral hydrogen atom has a wavelength of $656.1$ nm.

72.9\text{ nm}

164.0\text{ nm}

218.7\text{ nm}

656.1\text{ nm}

2 solutions

A Former Brilliant Member
Jan 1, 2019

We know the Rydberg Equation,

$\dfrac {1}{\lambda} = RZ^2 (\dfrac {1}{n_1^2} - \dfrac {1}{n_2^2})$

$R = 1.0967 \times 10^{-7} m^{-1}$ is the Rydberg constant, $Z$ the atomic number.

Therefore, $\dfrac {\lambda _{Li^{2+}}}{\lambda _H^+} = \dfrac {Z_{H^+}^2}{Z_{Li^{2+}}^2} \Rightarrow \lambda _{Li^{+2}} = {656.1}\times \dfrac {1^2}{3^2} = \boxed {72.9 nm}$

Shivam Hinduja
Dec 24, 2014

The energy during the transition between the shell n=2 and n=3 in lithium atom would be nine times to that of hydrogen atom.

Hence, The wavelength becomes one-nineth of wavelength in hydrogen atom during the transition.

Atomic spectra

2 solutions

0 pending reports