Microwaves have frequencies in the range 10^9to 10^12/s (cycles per second) equivalent to between 1 gigahertz and 1 terahertz. What is the wave length of microwave radiation whose frequency is 1.258 X 10^10/s?

How do I solve this problem

Worked the same as your next problem. The speed of light is 3E8 m/s

2.38×10^-2 m to 2.38×10^7 nm

To solve this problem, you can use the formula:

wavelength = speed of light / frequency

The speed of light is approximately 3 x 10^8 meters per second.

Step 1: Write down the given values:
Frequency = 1.258 x 10^10/s
Speed of light = 3 x 10^8 m/s

Step 2: Plug in the values into the formula:
wavelength = (3 x 10^8 m/s) / (1.258 x 10^10/s)

Step 3: Simplify the equation by dividing the numerator by the denominator:
wavelength = (3 / 1.258) x (10^8 / 10^10) m

Step 4: Simplify further by performing the calculations:
wavelength = 2.384 x (10^8 / 10^10) m

Step 5: Simplify the final calculation:
wavelength = 2.384 x 10^-2 m

Thus, the wavelength of the microwave radiation with a frequency of 1.258 x 10^10/s is approximately 2.384 x 10^-2 meters.

To solve this problem, you can use the formula that relates wavelength (λ), frequency (f), and the speed of light (c). The formula is:

c = λf

where c is the speed of light, which is approximately 3.00 × 10^8 meters per second (m/s).

To find the wavelength (λ), rearrange the formula:

λ = c / f

Now, plug in the given frequency (f = 1.258 × 10^10/s) and the speed of light (c = 3.00 × 10^8 m/s) into the formula:

λ = (3.00 × 10^8 m/s) / (1.258 × 10^10/s)

To simplify this expression, divide the numerator by the denominator:

λ ≈ 0.0238 meters

Therefore, the wavelength of microwave radiation with a frequency of 1.258 × 10^10/s is approximately 0.0238 meters or 23.8 millimeters.