Atoms And Nuclei Question 293
Question: The element which has a $ {K_{\alpha }} $ x-rays line of wavelength 1.8 A is ( $ R=1.1\times {{10}^{-7}}{{m}^{-1}},b=1 $ and $ \sqrt{5/33}=0.39 $ )
Options:
A) Co, Z=27
B) Iron, Z=26
C) Mn, Z=25
D) Ni, Z=28
Show Answer
Answer:
Correct Answer: A
Solution:
- $ \frac{1}{{\lambda_{\alpha }}}=\frac{3R}{4}{{( Z-1 )}^{2}} $
$ \Rightarrow ( Z-1 )=\sqrt{\frac{4}{3R{\lambda_{\alpha }}}}=\sqrt{\frac{4}{3\times 1.1\times 10^{7}\times 1.8\times {{10}^{-10}}}} $ $ =\frac{200}{3}\sqrt{\frac{5}{33}}=\frac{78}{3}=26 $
$ \Rightarrow Z=26+1=27 $
