Match List I with List II, atoms, (Spectral lines of hydrogen for transitions from) [2024]

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Solution

Q.
Match List I with List II [2024]

List-I List-II

(Spectral lines of hydrogen for transitions from) (Wavelengths (nm))

A. $n_{2}$ = 3 to $n_{1}$ = 2 I. 410.2

B. $n_{2}$ = 4 to $n_{1}$ = 2 II. 434.1

C. $n_{2}$ = 5 to $n_{1}$ = 2 III. 656.3

D. $n_{2}$ = 6 to $n_{1}$ = 2 IV. 486.1

Choose the correct answer from the options given below.

1 A-II, B-I, C-IV, D-III

2 A-III, B-IV, C-II, D-I

3 A-IV, B-III, C-I, D-II

4 A-I, B-II, C-III, D-IV

Ans.
(2)

Wavelength of spectral lines of hydrogen is given by $\frac{1}{λ} = R [\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}}]$

For $n_{2} = 3$ to $n_{1} = 2$

$\frac{1}{λ} = 1.09 \times 10^{7} [\frac{1}{{(2)}^{2}} - \frac{1}{{(3)}^{2}}]$

$λ = 656.3$ $nm$

$A \to III$

For $n_{2} = 4$ to $n_{1} = 2$

$\frac{1}{λ} = 1.09 \times 10^{7} [\frac{1}{{(2)}^{2}} - \frac{1}{{(4)}^{2}}] \Rightarrow λ = 486.1$ $nm$

$B \to IV$

For $n_{2} = 5$ to $n_{1} = 2$

$\frac{1}{λ} = 1.09 \times 10^{7} [\frac{1}{{(2)}^{2}} - \frac{1}{{(5)}^{2}}] \Rightarrow λ = 434.1$ $nm$

$C \to II$

For $n_{2} = 6$ to $n_{1} = 2$

$\frac{1}{λ} = 1.09 \times 10^{7} [\frac{1}{{(2)}^{2}} - \frac{1}{{(6)}^{2}}] \Rightarrow λ = 410.2$ $nm$

$D \to I$

Option (2) is correct

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