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NEET 2011
Exam
NEET
Year
2011
Subject
Physics
Chapter
Atomic Physics

NEET 2011 · Physics · Atomic Physics

The wavelength of the first line of Lyman series for hydrogen atom...

The wavelength of the first line of Lyman series for hydrogen atom is equal to that of the second line of Balmer series for a hydrogen like ion. The atomic number ZZ of hydrogen like ion is

Options

  1. A4
  2. B1
  3. C2
  4. D3

Correct answer

C. 2

Step-by-step solution

Lyman series for H\mathrm{H}-ion hcλ=\frac{h c}{\lambda}=R h c\left(\frac{1}{1^2}-\frac{1}{2^2}\right)AndforH−likeionAnd for H-like ionhcλ=Z2Rhc(122−142)∴(112−122)=Z2(14−116)(1−14)=Z2(14−116)Z=2\begin{aligned}\frac{h c}{\lambda}& =Z² R h c\left(\frac{1}{2^2}-\frac{1}{4^2}\right)\\ \therefore \quad\left(\frac{1}{1^2}-\frac{1}{2^2}\right)& =Z²\left(\frac{1}{4}-\frac{1}{16}\right)\\ \left(1-\frac{1}{4}\right)& =Z²\left(\frac{1}{4}-\frac{1}{16}\right)\\ Z & =2 \end{aligned}$
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