Atoms And Nuclei Question 266
Question: The wavelength $ {K_{\alpha }} $ of X-rays for two metals ‘A’ and ?B? are $ \frac{4}{1875R} $ and $ \frac{1}{675R} $ respectively, where ‘R’ is Rydberg constant. Find the number of elements lying between A and B according to their atomic numbers
Options:
A) 3
B) 1
C) 4
D) 5
Show Answer
Answer:
Correct Answer: C
Solution:
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Using v $ \frac{1}{\lambda }=R{{( Z-1 )}^{2}}[ \frac{1}{n_{2}^{2}}-\frac{1}{n_{1}^{2}} ] $ For $ \alpha $ particle, $ n_{1}=2,n_{2}=1 $
For metal A: $ \frac{1875R}{4}=R{{( Z_{1}-1 )}^{2}}( \frac{3}{4} )\Rightarrow Z_{1}=26 $
For metal B: $ 675R=R{{( Z_{2}-1 )}^{2}}( \frac{3}{4} )\Rightarrow Z_{2}=31 $
Therefore, 4 elements lie between A and B.
