question_answer

A standing wave having 3 nodes and 2 antinodes is formed between two atoms having a distance \[1.21\,\overset{o}{\mathop{A}}\,\] between them. The wavelength of the standing wave is:              [AIPMT 1998]

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

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

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

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

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 \[2\left( \frac{\lambda }{2} \right)\]

\[\therefore \]    \[2\frac{\lambda }{2}=1.21\,{\AA}\]

\[\Rightarrow \]   \[\lambda =1.21\,{\AA}\]