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

Explanation

To find the wavelength corresponding to a radio frequency of 400 MHz, we can use the formula that relates wavelength (λ), frequency (ν), and the speed of light (c):

### Step-by-Step Solution:

1. **Identify the given frequency**:
The frequency (ν) is given as 400 MHz. We need to convert this into Hertz (Hz):
\[ 400 \text{ MHz} = 400 \times 10^6 \text{ Hz} = 4 \times 10^8 \text{ Hz} \]

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

3. **Apply the wavelength formula**:
The relationship between wavelength (λ), frequency (ν), and the speed of light (c) is given by the formula:
\[ \lambda = \frac{c}{ν} \]

4. **Substitute the values into the formula**:
Now we can substitute the values of c and ν into the formula:
\[ \lambda = \frac{3 \times 10^8 \text{ m/s}}{4 \times 10^8 \text{ Hz}} \]

5. **Calculate the wavelength**:
Performing the division:
\[ \lambda = \frac{3}{4} \text{ m} = 0.75 \text{ m} \]

6. **Final answer**:
Therefore, the wavelength corresponding to the 400 MHz radio frequency is:
\[ \lambda = 0.75 \text{ m} \]