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AIIMS 201827 May
Exam
AIIMS
Year
2018
Date
27 May
Subject
Chemistry
Chapter
Structure of Atom

AIIMS 2018 · 27 May · Chemistry · Structure of Atom

What is the maximum wavelength of line of Balmer series of hydrogen...

What is the maximum wavelength of line of Balmer series of hydrogen spectrum? (R=1.09×107 m−1)\left(R=1.09 \times 10^7 \mathrm{~m}^{-1}\right)

Options

  1. A400 nm400 \mathrm{~nm}
  2. B660 nm660 \mathrm{~nm}
  3. C486 nm486 \mathrm{~nm}
  4. D434 nm434 \mathrm{~nm}

Correct answer

B. 660 nm660 \mathrm{~nm}

Step-by-step solution

For maximum wavelength in the Balmer series, n2=3andn1=2n_2=3 and n_1=2. ∴1λ=1.09×107×12(122−132)⇒1λ=1.09×107×1(14−19)=1.09×107×1(536)⇒λ=365×1.09×107 m=6.60×10−7 m=660 nm\begin{aligned} \therefore \quad \frac{1}{\lambda} & =1.09 \times 10^7 \times 1^2\left(\frac{1}{2^2}-\frac{1}{3^2}\right) \\ \Rightarrow \quad \frac{1}{\lambda} & =1.09 \times 10^7 \times 1\left(\frac{1}{4}-\frac{1}{9}\right) \\ & =1.09 \times 10^7 \times 1\left(\frac{5}{36}\right) \\ \Rightarrow \lambda & =\frac{36}{5 \times 1.09 \times 10^7} \mathrm{~m} \\ & =6.60 \times 10^{-7} \mathrm{~m}=660 \mathrm{~nm}\end{aligned}
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