A) \[C\xrightarrow[{}]{{{H}_{2}}O}D\]
B) \[n=3,\text{ }l=1,\text{ }m=1,\text{ }s=+\text{ }1/2\]
C) \[n=3,l=2,m=1,s=+1/2\]
D) \[n=4,\text{ }l=0,\text{ }m=0,\text{ }s=+\text{ }1/2\]
Correct Answer: D
Solution :
Since, a line makes an angle of\[\frac{\pi }{4}\]with positive direction of each of X-axis and Y-axis, therefore \[\alpha =\frac{\pi }{4},\beta =\frac{\pi }{4}\] We know that, \[co{{s}^{2}}\alpha +co{{s}^{2}}\beta +co{{s}^{2}}\gamma =1\] \[\Rightarrow \]\[{{\cos }^{2}}\frac{\pi }{4}+{{\cos }^{2}}\frac{\pi }{4}+{{\cos }^{2}}\gamma =1\] \[\Rightarrow \]\[\frac{1}{2}+\frac{1}{2}+{{\cos }^{2}}\gamma =1\] \[\Rightarrow \]\[{{\cos }^{2}}\gamma =0\]\[\Rightarrow \]\[\gamma ={{90}^{o}}\]
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