If ν1 is the frequency of series limit of Lyman series, ν2 is the frequency of first line of Lyman series and ν3 be the frequency of the series limit of Balmer series. Then

Question

If ν1 is the frequency of series limit of Lyman series, ν2 is the frequency of first line of Lyman series and ν3 be the frequency of the series limit of Balmer series. Then (A) ν1+ν2=ν3 (B) ν2-ν1=ν3 (C) ν1-ν2=ν3 (D) v3=(1/2)(v1+v2)

Tardigrade Admin · Accepted Answer

beginarrayl v1= cR ((1/12)-(1/∞2))= cR v2= cR ((1/12)-(1/22))=(3 cR /4) v3= cR ((1/22)-∞)=( cR /4) endarray So v1-v2=v3

Q. If $ν_{1}$ is the frequency of series limit of Lyman series, $ν_{2}$ is the frequency of first line of Lyman series and $ν_{3}$ be the frequency of the series limit of Balmer series. Then

$ν_{1} + ν_{2} = ν_{3}$

$ν_{2} - ν_{1} = ν_{3}$

$ν_{1} - ν_{2} = ν_{3}$

$v_{3} = \frac{1}{2} (v_{1} + v_{2})$

$v_{1} = c R (\frac{1}{1 ^{2}} - \frac{1}{\infty ^{2}}) = c R v_{2} = c R (\frac{1}{1 ^{2}} - \frac{1}{2 ^{2}}) = \frac{3 c R}{4} v_{3} = c R (\frac{1}{2 ^{2}} - \infty) = \frac{c R}{4}$
So $v_{1} - v_{2} = v_{3}$

Q. If ν1​ is the frequency of series limit of Lyman series, ν2​ is the frequency of first line of Lyman series and ν3​ be the frequency of the series limit of Balmer series. Then

ν1​+ν2​=ν3​

ν2​−ν1​=ν3​

ν1​−ν2​=ν3​

v3​=21​(v1​+v2​)