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NCERT Class XI Chemistry Structure of Atom Solutions

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Question : 50 of 67
Marks: +1, -0
The longest wavelength doublet absorption transition is observed at 589 and 589.6 nm. Calculate the frequency of each transition and energy difference between two excited states.
Solution:  
Step I : Wavelength (λ) = 589 nm = 589 × 10−9 m10^{-9}\,\text{m}
Frequency (u) = cλ\frac{c}{\lambda} = 3×108589×10−9\frac{3\times10^8}{589\times10^{-9}} = 50.93 × 101410^{14} cycles per sec
Step II : Wavelength (λ) = 589.6 nm = 589.6 × 10−9 m10^{-9}\,\text{m}
∴ v = cλ\frac{c}{\lambda} = 3×108589.6×10−9\frac{3\times10^8}{589.6\times10^{-9}} = 5.088 × 101410^{14} cycles per sec
Energy difference between two excited states,
ΔE = 6.626 × 10−3410^{-34} (5.093 – 5.088) 101410^{14} = 6.626 × 10−3410^{-34} × 5 × 10−310^{-3} × 101410^{14}
= 3.31 × 10−22 J10^{-22}\,\text{J}
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