The frequency `1057 MHz` of radiation arising from two close energy levels in hydrogen belong to:

Options

A. Infrared rays
B. X-rays
C. `gamma`-rays
D. Radio waves

Explanation

To determine the region of the electromagnetic spectrum that corresponds to the frequency of 1057 MHz, we can follow these steps:

### Step-by-Step Solution:

1. **Convert the Frequency to Hertz**:
The given frequency is 1057 MHz. To convert this to Hertz, we use the conversion factor that 1 MHz = \(10^6\) Hz.
\[ 1057 \text{ MHz} = 1057 \times 10^6 \text{ Hz} = 1.057 \times 10^9 \text{ Hz} \]

2. **Identify the Frequency Ranges of Different Regions**:
We need to know the frequency ranges for various regions of the electromagnetic spectrum:
- **Radio Waves**: \(3 \times 10^3 \text{ Hz} \) to \(3 \times 10^{11} \text{ Hz}\)
- **Infrared**: \(3 \times 10^{11} \text{ Hz} \) to \(4.3 \times 10^{12} \text{ Hz}\)
- **Visible Light**: \(4.3 \times 10^{14} \text{ Hz} \) to \(7.5 \times 10^{14} \text{ Hz}\)
- **Ultraviolet**: \(7.5 \times 10^{14} \text{ Hz} \) to \(3 \times 10^{16} \text{ Hz}\)
- **X-rays**: \(3 \times 10^{16} \text{ Hz} \) to \(3 \times 10^{19} \text{ Hz}\)
- **Gamma Rays**: Greater than \(10^{19} \text{ Hz}\)

3. **Determine Where 1.057 x 10^9 Hz Fits**:
Now we compare \(1.057 \times 10^9 \text{ Hz}\) with the ranges we have:
- It is **greater than** \(3 \times 10^3 \text{ Hz}\) (the lower limit of radio waves).
- It is **less than** \(3 \times 10^{11} \text{ Hz}\) (the upper limit of radio waves).
- It does not fit into the infrared range, as it is less than \(3 \times 10^{11} \text{ Hz}\).

4. **Conclusion**:
Since \(1.057 \times 10^9 \text{ Hz}\) falls within the range of radio waves, we conclude that the frequency of 1057 MHz corresponds to the radio wave region of the electromagnetic spectrum.

### Final Answer:
The frequency of 1057 MHz of radiation arising from two close energy levels in hydrogen belongs to the **radio wave** region of the electromagnetic spectrum.

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