The `MRI` (magnetic resonance imaging) body scanners used in hospitals operate with `400 MH`z radio frequency. The wavelength corresponding to this radio frequency is.

Options

A. 0.75 m
B. 0.75 cm
C. 1.5 m
D. 2 cm

Explanation

To find the wavelength corresponding to the 400 MHz radio frequency used in MRI scanners, we can use the relationship between the speed of light, frequency, and wavelength. The formula we will use is:

\[ c = \lambda \cdot f \]

Where:
- \( c \) is the speed of light (approximately \( 3 \times 10^8 \) m/s),
- \( \lambda \) is the wavelength (in meters),
- \( f \) is the frequency (in Hz).

### Step-by-Step Solution:

1. **Convert Frequency from MHz to Hz**:
The given frequency is 400 MHz. To convert this to Hz:
\[ f = 400 \, \text{MHz} = 400 \times 10^6 \, \text{Hz} \]

2. **Use the Speed of Light**:
The speed of light \( c \) is approximately:
\[ c = 3 \times 10^8 \, \text{m/s} \]

3. **Rearrange the Formula to Solve for Wavelength**:
We can rearrange the formula \( c = \lambda \cdot f \) to solve for \( \lambda \):
\[ \lambda = \frac{c}{f} \]

4. **Substitute the Values**:
Now we substitute the values of \( c \) and \( f \) into the equation:
\[ \lambda = \frac{3 \times 10^8 \, \text{m/s}}{400 \times 10^6 \, \text{Hz}} \]

5. **Calculate the Wavelength**:
Performing the calculation:
\[ \lambda = \frac{3 \times 10^8}{400 \times 10^6} = \frac{3}{400} \, \text{m} = 0.0075 \, \text{m} = 0.75 \, \text{cm} \]

Thus, the wavelength corresponding to the 400 MHz radio frequency is **0.75 meters**.