Question

Let ${\vartheta }_1$ be the frequency of the series limit of the Lyman series and ${\vartheta }_2$ be the frequency of the first line of the Lyman series ${\vartheta }_3$ be the frequency of the series limit of Balmar series, then

• A. ${\vartheta }_1–{\vartheta }_2={\vartheta }_3$
  
• B. ${\vartheta }_2-{\vartheta }_1={\vartheta }_3$
  
• C. $2{\vartheta }_3={\vartheta }_1+{\vartheta }_2$
  
• D. ${\vartheta }_1={\vartheta }_2-{\vartheta }_3$

Answer 1

The correct option is A ${\vartheta }_1–{\vartheta }_2={\vartheta }_3$


$E_{\infty }-E_1=h{\nu }_1....\left(1\right)$
$E_{\infty }-E_2=h{\nu }_3....\left(2\right)$
$E_2-E_1=h{\nu }_2....\left(3\right)$
(1) - (2)
$E_2-E_1=h[{\nu }_1-{\nu }_3]....\left(4\right)$
From (3) and (4)
$h{\nu }_2=h[{\nu }_1-{\nu }_3]$
${\nu }_3={\nu }_1-{\nu }_2$