Dual Nature Of Light Question 105
Question: The X-ray wavelength of $ {L_{\alpha }} $ line of platinum (Z=78) is $ 1.30{AA}. $ The X ?ray wavelength of $ {L_{\alpha }} $ line of Molybdenum (Z=42) is [EAMCET (Eng.) 2000]
Options:
A) 5.41 $ \overset{o}{\mathop{A}}, $
B) 4.20 $ \overset{o}{\mathop{A}}, $
C) 2.70 $ \overset{o}{\mathop{A}}, $
D) 1.35 $ \overset{o}{\mathop{A}}, $
Show Answer
Answer:
Correct Answer: A
Solution:
The wave length of $ {L_{\alpha }} $ line is given by $ \frac{1}{\lambda }=R,{{(z-7.4)}^{2}},( \frac{1}{2^{2}}-\frac{1}{3^{2}} ),\Rightarrow \lambda \propto \frac{1}{{{(Z-7.4)}^{2}}} $
$ \Rightarrow \frac{{\lambda_{1}}}{{\lambda_{2}}}=\frac{{{(z_{2}-7.4)}^{2}}}{{{(z_{1}-7.4)}^{2}}} $
$ \Rightarrow \frac{1.30}{{\lambda_{2}}}=\frac{{{(42-7.4)}^{2}}}{{{(78-7.4)}^{2}}} $
$ \Rightarrow ,{\lambda_{2}}=5.41,{\AA} $
BETA
