A standing wave, having `5` nodes and `4` antinodes is formed between two atoms having a distance `1.21Å` between them. The wavelength of the standing wave is

Options

A. `1.21Å`
B. `2.42Å`
C. `6.05Å`
D. `0.605Å`

Explanation

To find the wavelength of the standing wave formed between two atoms that are 1.21 Å apart, with 5 nodes and 4 antinodes, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Nodes and Antinodes**:
- In a standing wave, nodes are points where there is no displacement, while antinodes are points of maximum displacement.
- The given standing wave has 5 nodes and 4 antinodes.

2. **Identifying the Relationship**:
- The number of nodes (N) and antinodes (A) in a standing wave is related by the formula:
\[ N = A + 1 \]
- Here, we have 5 nodes and 4 antinodes, which confirms the relationship:
\[ 5 = 4 + 1 \]

3. **Calculating the Number of Wavelengths**:
- The distance between two consecutive nodes is half a wavelength (λ/2).
- The total distance between the first and the last node (5 nodes) can be calculated as:
\[ \text{Total distance} = \text{Number of intervals between nodes} \times \frac{\lambda}{2} \]
- The number of intervals between 5 nodes is 4 (since there are 4 gaps between 5 nodes).

4. **Setting Up the Equation**:
- Therefore, the total distance between the two atoms (1.21 Å) can be expressed as:
\[ 1.21 \, \text{Å} = 4 \times \frac{\lambda}{2} \]
- Simplifying this gives:
\[ 1.21 \, \text{Å} = 2\lambda \]

5. **Solving for Wavelength (λ)**:
- Rearranging the equation to find λ:
\[ \lambda = \frac{1.21 \, \text{Å}}{2} = 0.605 \, \text{Å} \]

### Final Answer:
The wavelength of the standing wave is **0.605 Å**.

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