Calculate the ratio of wavelength of first and the ultimate line of Balmer series of Li2+ - Chemistry - Structure of Atom

Question

Calculate the ratio of wavelength of first and the ultimate line
of Balmer series of Li2+?

Kanika Dalal · Accepted Answer

Dear Student,

The first line of Balmer series is obtained when transition occurs from n₂ = 3 to n₁ = 2.

$\frac{1}{λ_{F i r s t}} = 109677 [\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}}] \frac{1}{λ_{F i r s t}} = 109677 [\frac{1}{2^{2}} - \frac{1}{3^{2}}] \frac{1}{λ_{F i r s t}} = 109677 [\frac{1}{4} - \frac{1}{9}] (1)$

The ultimate line of Balmer series is obtained when transition occurs from n₂ = ∞ to n₁ = 2.

$\frac{1}{λ_{U l t i m a t e}} = 109677 [\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}}] \frac{1}{λ_{U l t i m a t e}} = 109677 [\frac{1}{2^{2}} - \frac{1}{\infty^{2}}] \frac{1}{λ_{U l t i m a t e}} = 109677 [\frac{1}{4} - 0] (2)$

To find the ratio of wavelength of first and the ultimate line, we divide equation (1) by equation (2).

$\frac{λ_{f i r s t}}{λ_{u l t i m a t e}} = \frac{1}{4} x \frac{36}{5} \frac{λ_{f i r s t}}{λ_{u l t i m a t e}} = \frac{9}{5}$

Hope its clear now.

Enjoy learning!!

Calculate the ratio of wavelength of first and the ultimate line of Balmer series of Li2+?

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