A) \[5.2\overset{\text{o}}{\mathop{\text{A}}}\,\]
B) \[4.6\overset{\text{o}}{\mathop{\text{A}}}\,\]
C) \[3.5\overset{\text{o}}{\mathop{\text{A}}}\,\]
D) \[2.1\overset{\text{o}}{\mathop{\text{A}}}\,\]
Correct Answer: D
Solution :
The given, \[\lambda =2.1\times {{10}^{-7}}m\] \[{{K}_{B}}=1.4\times {{10}^{-23}}J/K\] For STP \[T={{0}^{o}}C+273=273\,K\] \[P=1\,atm=1.01\times {{10}^{5}}N/{{m}^{2}}\] \[d=?\] \[\lambda =\frac{{{K}_{B}}T}{\sqrt{2}\,\pi {{d}^{2}}\times P}\] \[=\frac{1.4\times {{10}^{-23}}\times 273}{1.41\times 3.14\times 2.1\times {{10}^{-7}}\times 1.01\times {{10}^{5}}}\] \[=\frac{382.2}{9.39}\times {{10}^{-21}}\] \[{{d}^{2}}=40.7\times {{10}^{-21}}=4.07\times {{10}^{-20}}\] \[d=\sqrt{4.07\times {{10}^{-20}}}=2.01\times {{10}^{-10}}\] \[d=2.01\,\overset{o}{\mathop{A}}\,\] \[d\cong 2.1\,\overset{o}{\mathop{A}}\,\]
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