A beam of monochromatic light is used to excite the electron in ${Li}^{+ +}$ from the first orbit to the third orbit. The wavelength of monochromatic light is found to be $x \times 10^{- 10} m$ . The value of $x$ is _____ .
[Given $h c = 1242 eV nm$ ]

Question

A beam of monochromatic light is used to excite the electron in ${Li}^{+ +}$ from the first orbit to the third orbit. The wavelength of monochromatic light is found to be $x \times 10^{- 10} m$ . The value of $x$ is _____ .

[Given $h c = 1242 eV nm$ ]

TestHub · Accepted Answer

Energy released in the transition will be,

$Δ E = 13.6 \times Z^{2} [\frac{1}{1^{2}} - \frac{1}{3^{2}}]$ $= 13.6 \times 3^{2} \times \frac{8}{9} eV = 108.8 eV$

Now energy of photon can be written as,

$\frac{h c}{λ} = 108.8 eV \Rightarrow λ = \frac{12400}{108.8} \overset{o}{A} \approx 114 \overset{o}{A}$

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