**Frequency and Wavelength Relationship**
Frequency and wavelength are two important properties of waves. They are inversely proportional to each other, meaning that as the frequency of a wave increases, its wavelength decreases. This relationship is described by the equation:

c = λ * f

Where:
c = speed of light (approx. 3 x 10^8 m/s)
λ = wavelength
f = frequency

**Calculating Wavelength**
Given that the frequency of the radiation is 1000 Hz, we can use the equation mentioned above to calculate the wavelength.

c = λ * f

Rearranging the equation, we get:

λ = c / f

Substituting the known values:

λ = (3 x 10^8 m/s) / (1000 Hz)

Simplifying the equation:

λ = 3 x 10^5 m

**Converting Wavelength**
The calculated wavelength is in meters. However, the options provided for the answer are in different units. We need to convert the wavelength to match the units in the options.

- a) 3 x 10^-13: This option is in meters, and it is much smaller than the calculated wavelength. Therefore, it is not the correct answer.
- b) 3.0 x 10^7: This option is in meters, and it is much larger than the calculated wavelength. Therefore, it is not the correct answer.
- c) 3000 A: This option is in angstroms (A), which is a unit commonly used for measuring atomic distances. To convert meters to angstroms, we use the conversion factor 1 m = 10^10 A. Applying the conversion:

λ = 3 x 10^5 m * (10^10 A / 1 m) = 3 x 10^15 A

- d) 300 nm: This option is in nanometers (nm), which is another commonly used unit for measuring wavelengths. To convert meters to nanometers, we use the conversion factor 1 m = 10^9 nm. Applying the conversion:

λ = 3 x 10^5 m * (10^9 nm / 1 m) = 3 x 10^14 nm

**Conclusion**
The correct answer is option d) 300 nm. The wavelength of the radiation with a frequency of 1000 Hz is approximately 300 nanometers.

Formula
speed= frequency× wavelength

speed of radiation 3×10⁸
so wavelength = speed/ frequency
. = 3×10⁸/1000
=3×10⁵ m