question_answer

                  A standing wave having 3 nodes and 2 antinodes is formed between two atoms having a distance \[1.21\,\overset{\text{o}}{\mathop{\text{A}}}\,\] between them. The wavelength of the standing wave is:                                                                               

A)                 \[1.21\,\overset{\text{o}}{\mathop{\text{A}}}\,\]

B)                 \[1.42\,\overset{\text{o}}{\mathop{\text{A}}}\,\]                          

C)                 \[6.05\,\overset{\text{o}}{\mathop{\text{A}}}\,\]                          

D)                 \[3.63\,\overset{\text{o}}{\mathop{\text{A}}}\,\]

Correct Answer: A

Solution :

                                          Key Idea: The given standing wave has 2 segments.                 The given standing wave has shown in the figure.                                 As length of one loop or segment is \[\frac{\lambda }{2}\], so length of 2 segments is \[2\left( \frac{\lambda }{2} \right)\] \[\therefore 2\frac{\lambda }{2}=1.21\,{\AA}\] \[\Rightarrow \lambda =1.21\,{\AA}\]