Question 413: Atoms & Nuclei

Question

The frequencies for series limit of Balmer and Paschen series are ' $\mathrm{V}_1$ ' and ' $\mathrm{V}_3$ ' respectively. If frequency of first line of Balmer series ' $\mathrm{V}_2$ ' then the relation between $V_1, V_2$ and $V_3$ is

Accepted Answer

$$ v=R Z^2\left(\frac{1}{n^2}-\frac{1}{m^2}ight) $$
Series limit of Balmer: $\mathrm{n}=2, \mathrm{~m}=\infty$
$$ 	herefore \mathrm{v}_1=\frac{\mathrm{RZ}^2}{4} $$
Series limit of Paschen: $\mathrm{n}=3, \mathrm{~m}=\infty$
$$ 	herefore \quad v_2=\frac{R Z^2}{9} $$
$1^{	ext {st }}$ line of Balmer series: $\mathrm{n}_1=2, \mathrm{n}_2=3$
$$ 	herefore \quad \mathrm{v}_3=\mathrm{RZ}^2\left(\frac{1}{2^2}-\frac{1}{3^2}ight)=\frac{\mathrm{RZ}^2}{4}-\frac{\mathrm{RZ}^2}{9}=\mathrm{v}_1-\mathrm{v}_2 $$

Answer

$\mathrm{v}_1-\mathrm{v}_3=2 \mathrm{v}_1$

Answer

$v_1+v_2=v_3$

Answer

$\mathrm{v}_1-\mathrm{v}_2=\mathrm{v}_3$

Answer

$v_1+v_3=v_2$

Atoms & Nuclei

The frequencies for series limit of Balmer and Paschen series are ' \mathrm{V}_1 ' and ' \mathrm{V}_3 ' respectively. If frequency of first line of Balmer series ' \mathrm{V}_2 ' then the relation between V_1, V_2 and V_3 is

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