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| 1. |
The ground state energy of hydrogen atom is - 13.6 eV. If an electron makes a transition from an energy level - 0.85 eV to -3.4 eV, calculate the wavelength of the spectral line emitted. To which series of hydrogen spectrum does this wavelength belong? |
| Answer» <html><body><p></p>Solution :The groundstateenergy of hydrogen `E_(1)`= 13.6 eV . <br/> `therefore ` Energy `E_(i) = -0.85e <a href="https://interviewquestions.tuteehub.com/tag/v-722631" style="font-weight:bold;" target="_blank" title="Click to know more about V">V</a>` <a href="https://interviewquestions.tuteehub.com/tag/corresponds-935737" style="font-weight:bold;" target="_blank" title="Click to know more about CORRESPONDS">CORRESPONDS</a> to a level `n_(i)`where ` - 0.85 = (-13.6)/(n_(i)^(2)) rArr n_(i) = 4` <br/>Againenergy `E_(f) = - 3.4` eV correspondsto a level `n_(f)`suchthat ` -3.4 = - (13.6)/(n_(f)^(2))`, which leads us totheresult `n_(f) = 2` <br/> As transition is takingplace from `n_(i) = 4`level to `n_(f) = 2` levelthewavelenghtbelongs to Balmer series of hydrogen <a href="https://interviewquestions.tuteehub.com/tag/spectrum-1221793" style="font-weight:bold;" target="_blank" title="Click to know more about SPECTRUM">SPECTRUM</a> . <br/>The wavelenghtof spectrall lineis given by therelation. <br/> `hv = (<a href="https://interviewquestions.tuteehub.com/tag/hc-1016346" style="font-weight:bold;" target="_blank" title="Click to know more about HC">HC</a>)/(lambda) = E_(i) = E_(f) =- 0.85 eV - (-3.4 eV) = + 2.55 eV`. <br/>`therefore "" lambda = (hc)/(2.55ev) = (6.63 xx 10^(-34) xx 3 xx 10^(<a href="https://interviewquestions.tuteehub.com/tag/8-336412" style="font-weight:bold;" target="_blank" title="Click to know more about 8">8</a>))/((2.55 xx 1.60 xx 10^(-19))J)= 4.875 xx 10^(-7) m = 487.5` nm</body></html> | |