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`        A 12·5 eV electron beam is used to excite a gaseous hydrogen atom atroom temperature. Determine the wavelengths and the correspondingseries of the lines emitted.`
one year ago

Arun
22545 Points
```							12.5 eV electron beam is used to bombard gaseous hydrogen at room temperature. Also, gaseous hydrogen in its ground state at RT = -13.6 eVSo, the energy of the gaseous hydrogen = -13.6 + 12.5 = -1.1 eVSo, orbital energy E = -13.6/ n2 eV  (where, n = 3)E = -13.6/ 32 = -13.6/9 = -1.5 eVIf the energy is equal to the energy of gaseous hydrogen. It can be concluded that the electron has jumped from n =1 to n - 3 levelIn de excitation process, electrons can jump from n=3 to n=1. then Lyman series as1/ λ = Ry (1/ 12-1/ n2) , where, Ry =  1.097 x 107 m/sWavelength of radiation emitted by transition of electronFor n=3,We can get1/ λ = 1.097 x 107 (1/ 12-1/ 32) = 1.097 x 107(1- 1/9) = 1.097 x 107x 8/9 = 102.55 nmIf the transmission from n=2 to n=1 , then,1/ λ = 1.097 x 107 (1/ 12-1/ 32) = 1.097 x 107(1- 1/4) = 1.097 x 107x 3/4 = 121.54 nmIf the transmission from n=3 to n=2 , then,1/ λ = 1.097 x 107 (1/ 22-1/ 32) = 1.097 x 107(1/4- 1/9) = 1.097 x 107x 5/36 = 656.33 nmHence, in Lyman series, two wavelengths i.e. 102.55 nm and 121.54 nm are emitted. In Balmer series, one wavelength, 656.33 nm is emitted.
```
one year ago
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