Dual Nature Of Light Question 101
Question: The wavelength of $ {K_{\alpha }} $ X-rays produced by an X-ray tube is 0.76 Å. The atomic number of the anode material of the tube is [IIT 1996]
Options:
A) 20
B) 60
C) 40
D) 80
Show Answer
Answer:
Correct Answer: C
Solution:
The wavelength of X-ray lines is given by Rydberg Formula $ \frac{1}{\lambda }=RZ^{2},( \frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}} ) $ For $ {K_{\alpha }} $ line, $ n_{1}=1 $ and $ n_{2}=2 $
$ \therefore \frac{1}{\lambda }=RZ^{2}( \frac{3}{4} ) $
$ \Rightarrow ,Z={{( \frac{4}{3R\lambda } )}^{1/,2}} $ $ ={{[ \frac{4}{3,(1.097\times 10^{7}{{m}^{-1}}),(0.76\times {{10}^{-10}}m)} ]}^{1/,2}} $ = 39.99 » 40
BETA
