A beam of monochromatic light is used to excite the electron in $L i^{++}$ from the first orbit to the third orbit. The wavelength of monochromatic light is found to be $x \times 1 0^{- 10} m$ . The value of $x$ is _____ .
[Given $h c = 1242 e Vnm$ ]

Question

A beam of monochromatic light is used to excite the electron in $L i^{++}$ from the first orbit to the third orbit. The wavelength of monochromatic light is found to be $x \times 1 0^{- 10} m$ . The value of $x$ is _____ .

[Given $h c = 1242 e Vnm$ ]

TestHub · Accepted Answer

Energy released in the transition will be,

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

Now energy of photon can be written as,

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

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