NEET-XII-Physics
43: Bohr's Model and Physics of the Atom
- #4In which of the following transitions will the wavelength be minimum?
(a) n = 5 to n = 4
(b) n = 4 to n = 3
(c) n = 3 to n = 2
(d) n = 2 to n = 1digAnsr: dAns : (d) n = 2 to n = 1
For the transition in the hydrogen-like atom, the wavelength of the emitted radiation is calculated by
`` \frac{1}{\lambda }=\,\mathrm{\,R\,}{Z}^{2}\left(\frac{1}{{n}_{1}}-\frac{1}{{n}_{2}}\right)``
Here, R is the Rydberg constant.
For the transition from n = 5 to n = 4, the wavelength is given by
`` \frac{1}{\lambda }=\,\mathrm{\,R\,}{Z}^{2}\left(\frac{1}{{4}^{2}}-\frac{1}{{5}^{2}}\right)``
`` \lambda =\frac{400}{9\,\mathrm{\,R\,}{Z}^{2}}``
For the transition from n = 4 to n = 3, the wavelength is given by
`` \frac{1}{\lambda }=\,\mathrm{\,R\,}{Z}^{2}\left(\frac{1}{{3}^{2}}-\frac{1}{{4}^{2}}\right)``
`` \lambda =\frac{144}{7\,\mathrm{\,R\,}{Z}^{2}}``
For the transition from n = 3 to n = 2, the wavelength is given by
`` \frac{1}{\lambda }=\,\mathrm{\,R\,}{Z}^{2}\left(\frac{1}{{2}^{2}}-\frac{1}{{3}^{2}}\right)``
`` \lambda =\frac{36}{5\,\mathrm{\,R\,}{Z}^{2}}``
For the transition from n = 2 to n = 1, the wavelength is given by
`` \frac{1}{\lambda }=\,\mathrm{\,R\,}{Z}^{2}\left(\frac{1}{{1}^{2}}-\frac{1}{{2}^{2}}\right)``
`` \lambda =\frac{2}{\,\mathrm{\,R\,}{Z}^{2}}``
From the above calculations, it can be observed that the wavelength of the radiation emitted for the transition from n = 2 to n = 1 will be minimum.
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