question_answer 75)

Calculate the wavelength for the emission transition if it starts from the orbit having radius 1.3225 nm and ends at 211.6 pm. Name the series to which this transition belongs and the region of the spectrum.

Answer:

We know, \[r=\frac{{{n}^{2}}}{Z}\times 0.529\overset{{}^\circ }{\mathop{\text{A}}}\,\] \[13.225=\frac{n_{2}^{2}}{Z}\times 0.529\overset{{}^\circ }{\mathop{\text{A}}}\,\] (i) \[2.116=\frac{n_{1}^{2}}{Z}\times 0.529\overset{{}^\circ }{\mathop{\text{A}}}\,\] (ii) (radii are taken in \[\overset{{}^\circ }{\mathop{\text{A}}}\,,{{n}_{2}}\] = higher orbit, \[{{n}_{1}}\] = lower orbit) Dividing Eqn. (i) by Eqn. (ii), we get: \[\frac{n_{2}^{2}}{n_{1}^{2}}=6.25\] \[\frac{{{n}_{2}}}{{{n}_{1}}}=2.5\] The line will lie in visible region.