if `lamda_(v'),lamda_(x)` and `lamda_(m)` represent the wavelengths of visible light X-rays and microwaves respectively then:

Options

A. `lamda_(m)gtlamda_(X)gtlambda_(v)`
B. `lamda_(v)gtlamda_(m)gtlambda_(x)`
C. `lamda_(m)gtlamda_(v)gtlambda_(x)`
D. `lamda_(v)gtlamda_(x)gtlambda_(m)`

Answer

To solve the question regarding the arrangement of the wavelengths of visible light (λv), X-rays (λx), and microwaves (λm), we will follow these steps:

### Step 1: Identify the Wavelength Ranges
We need to identify the specific wavelength ranges for each type of electromagnetic radiation:
- **Visible Light (λv)**: The wavelength range for visible light is approximately \(4 \times 10^{-7}\) m to \(7 \times 10^{-7}\) m.
- **X-rays (λx)**: The wavelength range for X-rays is approximately \(10^{-13}\) m to \(3 \times 10^{-8}\) m.
- **Microwaves (λm)**: The wavelength range for microwaves is approximately \(1 \times 10^{-3}\) m to \(3 \times 10^{-1}\) m.

### Step 2: Compare the Wavelengths
Next, we will compare the ranges of these wavelengths to determine their relative sizes:
- **Visible Light vs. X-rays**:
- The maximum wavelength of X-rays (\(3 \times 10^{-8}\) m) is much smaller than the minimum wavelength of visible light (\(4 \times 10^{-7}\) m). Thus, \(λx < λv\).

- **Visible Light vs. Microwaves**:
- The minimum wavelength of microwaves (\(1 \times 10^{-3}\) m) is much larger than the maximum wavelength of visible light (\(7 \times 10^{-7}\) m). Thus, \(λv < λm\).

- **X-rays vs. Microwaves**:
- The maximum wavelength of X-rays (\(3 \times 10^{-8}\) m) is still smaller than the minimum wavelength of microwaves (\(1 \times 10^{-3}\) m). Thus, \(λx < λm\).

### Step 3: Arrange the Wavelengths
Based on the comparisons made, we can arrange the wavelengths in order from smallest to largest:
- \(λx < λv < λm\)

### Final Arrangement
Thus, the final arrangement of the wavelengths is:
- **X-rays (λx)** < **Visible Light (λv)** < **Microwaves (λm)**

### Conclusion
The answer to the question is that the arrangement of the wavelengths is \(λx < λv < λm\).

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