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:

  • 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.



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