Some energy levels of a molecule are shown in the figure with their wavelengths of transitions. Then [2024]

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Q.
Some energy levels of a molecule are shown in the figure with their wavelengths of transitions. Then [2024]

1 $λ_{3} > λ_{2}, λ_{1} = 2 λ_{2}$

2 $λ_{3} > λ_{2}, λ_{1} = 4 λ_{2}$

3 $λ_{1} > λ_{2}, λ_{2} = 2 λ_{3}$

4 $λ_{2} > λ_{1}, λ_{2} = 2 λ_{3}$

Ans.
(4)

As, $Δ E = E_{i} - E_{f}$ and $λ = \frac{h c}{Δ E}$

$Δ E_{1} = \frac{- 5 E}{2} - (- 4 E) = \frac{3 E}{2}$

$λ_{1} = \frac{h c}{Δ E_{1}} = \frac{2 h c}{3 E}$ ...(i)

$Δ E_{2} = - 2 E - (- 3 E) = - 2 E + 3 E = E$

$λ_{2} = \frac{h c}{Δ E_{2}} = \frac{h c}{E}$ ...(ii)

$Δ E_{3} = - 2 E - (- 4 E) = - 2 E + 4 E = 2 E$

$λ_{3} = \frac{h c}{Δ E_{3}} = \frac{h c}{2 E}$ ...(iii)

From equation (i), (ii) and (iii)

$λ_{2} > λ_{1} > λ_{3} and λ_{2} = 2 λ_{3}$

Solution

Q.
Some energy levels of a molecule are shown in the figure with their wavelengths of transitions. Then [2024]

1 $λ_{3} > λ_{2}, λ_{1} = 2 λ_{2}$

2 $λ_{3} > λ_{2}, λ_{1} = 4 λ_{2}$

3 $λ_{1} > λ_{2}, λ_{2} = 2 λ_{3}$

4 $λ_{2} > λ_{1}, λ_{2} = 2 λ_{3}$

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Solution

Q. Some energy levels of a molecule are shown in the figure with their wavelengths of transitions. Then [2024]

1 λ3>λ2,λ1=2λ2

2 λ3>λ2,λ1=4λ2

3 λ1>λ2,λ2=2λ3

4 λ2>λ1,λ2=2λ3

Ans. (4) As, ΔE=Ei-Ef and λ=hcΔE ΔE1=-5E2-(-4E)=3E2 λ1=hcΔE1=2hc3E ...(i) ΔE2=-2E-(-3E)=-2E+3E=E λ2=hcΔE2=hcE ...(ii) ΔE3=-2E-(-4E)=-2E+4E=2E λ3=hcΔE3=hc2E ...(iii) From equation (i), (ii) and (iii) λ2>λ1>λ3 and λ2=2λ3

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Q.
Some energy levels of a molecule are shown in the figure with their wavelengths of transitions. Then [2024]

1 $λ_{3} > λ_{2}, λ_{1} = 2 λ_{2}$

2 $λ_{3} > λ_{2}, λ_{1} = 4 λ_{2}$

3 $λ_{1} > λ_{2}, λ_{2} = 2 λ_{3}$

4 $λ_{2} > λ_{1}, λ_{2} = 2 λ_{3}$