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  • is the frequency of the series limit of Lyman series, is the freq

\mathrm{v}_1 is the frequency of the series limit of Lyman series, \mathrm{v}_2 is the frequency of the first line of Lyman series and \mathrm{v}_3 is the frequency of the series limit of Balmer series. Then:

Option: 1

\mathrm{v_1-v_2=v_3}


Option: 2

\mathrm{v_1=v_2-v_3}


Option: 3

\mathrm{\frac{1}{v_2}=\frac{1}{v_1}+\frac{1}{v_3}}


Option: 4

\mathrm{\frac{1}{v_1}=\frac{1}{v_2}+\frac{1}{v_3}}


Answers (1)

best_answer

For Lyman series \mathrm{v}=\operatorname{Rc}\left[\frac{1}{1^2}-\frac{1}{\mathrm{n}^2}\right] \text { where } \mathrm{n}=2,3,4, \ldots

For the series limit of Lyman series, \mathrm{n=\infty}

\mathrm{\therefore \quad \mathrm{v}_1=\operatorname{Rc}\left[\frac{1}{1^2}-\frac{1}{\infty^2}\right]=\operatorname{Rc}}\: \: \: \: \: \: \: \: \: \: ......\mathrm{(i)}

For the first line of Lyman series, \mathrm{n = 2}

\mathrm{\therefore \quad v_2=\operatorname{Rc}\left[\frac{1}{1^2}-\frac{1}{2^2}\right]=\frac{3}{4} \mathrm{Rc}}\: \: \: \: \: \: \: \: \: \: ....\mathrm{(ii)}

For Balmer series \mathrm{v}=\operatorname{Rc}\left[\frac{1}{2^2}-\frac{1}{\mathrm{n}^2}\right] \text { where } \mathrm{n}=3,4,5, \ldots

For the series limit of Balmer series, \mathrm{n=\infty}

\mathrm{\therefore \quad v_3=\operatorname{Rc}\left[\frac{1}{2^2}-\frac{1}{\infty^2}\right]=\frac{\operatorname{Rc}}{4}}\: \: \: \: \: \: \: \: \: ......\mathrm{(iii)}

From equations (i), (ii) and (iii), we get

\mathrm{v_1=v_2+v_3 \quad \text { or } \quad v_1-v_2=v_3}

Posted by

manish painkra

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