If λ1 and λ2 are the wavelengths of the third member of Lyman and first member of the Paschen series respectively, then the value of λ1: λ2 is :

Question

If λ1 and λ2 are the wavelengths of the third member of Lyman and first member of the Paschen series respectively, then the value of λ1: λ2 is : (A) 1: 9 (B) 7: 108 (C) 7: 135 (D) 1: 3

Tardigrade Admin · Accepted Answer

(1/λ1)= R [(1/12)-(1/42)] (1/λ2)= R [(1/32)-(1/42)] (λ1/λ2)=([(1/9)-(1/16)]/[1-(1)16])=(7/9 × 15) (λ1/λ2)=(7/135)

Q. If $λ_{1}$ and $λ_{2}$ are the wavelengths of the third member of Lyman and first member of the Paschen series respectively, then the value of $λ_{1} : λ_{2}$ is :

$1 : 9$

$7 : 108$

$7 : 135$

$1 : 3$

$\frac{1}{λ _{1}} = R [\frac{1}{1 ^{2}} - \frac{1}{4 ^{2}}]$
$\frac{1}{λ _{2}} = R [\frac{1}{3 ^{2}} - \frac{1}{4 ^{2}}]$
$\frac{λ _{1}}{λ _{2}} = \frac{[ \frac{1}{9} - \frac{1}{16} ]}{[ 1 - \frac{1}{16} ]} = \frac{7}{9 \times 15}$
$\frac{λ _{1}}{λ _{2}} = \frac{7}{135}$

Q. If λ1​ and λ2​ are the wavelengths of the third member of Lyman and first member of the Paschen series respectively, then the value of λ1​:λ2​ is :

1:9

7:108

7:135

1:3