The frequency for a series limit of Balmer and Paschen series respectively are $f_{1}$ and $f_{3}$ . If the frequency of the first line of Balmer series is $f_{2}$ then the relation between $f_{1}, f_{2}$ and $f_{3}$ is

Question

The frequency for a series limit of Balmer and Paschen series respectively are

f_{1}

and

f_{3}

. If the frequency of the first line of Balmer series is

f_{2}

then the relation between

f_{1}, f_{2}

and

f_{3}

is (A)

f_{1} - f_{2} = f_{3}

(B)

f_{1} + f_{3} = f_{2}

(C)

f_{1} + f_{2} = f_{3}

(D)

f_{2} - f_{3} = 2 f_{1}

Tardigrade Admin · Accepted Answer

c = f λ, \frac{1}{λ} = \frac{f}{c}

\frac{1}{λ} = R (\frac{1}{P^{2}} - \frac{1}{n^{2}})

\Rightarrow f = R c (\frac{1}{P^{2}} - \frac{1}{n^{2}})

\Rightarrow f_{2} = R c (\frac{1}{2^{2}} - \frac{1}{3^{2}}) = R c (\frac{1}{4} - \frac{1}{9}) = \frac{5 R c}{36}

f_{1} = R c (\frac{1}{2^{2}}) = \frac{R c}{4}

f_{3} = R c (\frac{1}{3^{2}}) = \frac{R c}{9}

∴ f_{1} - f_{3} = R c (\frac{1}{4} - \frac{1}{9})

∴ f_{1} - f_{3} = f_{2}

∴ f_{1} - f_{2} = f_{3}

Q. The frequency for a series limit of Balmer and Paschen series respectively are f1 and f3. If the frequency of the first line of Balmer series is f2 then the relation between f1, f2 and f3 is