Question

Certain x-rays have a frequency of 1.0×1019hz. calculate their wavelength in air.

Answer 1

The wavelength of X-rays with a frequency of 1.0 × 10^19 Hz in air is 3.00 × 10^-11 meters or 0.03 nanometers, calculated using the relationship between the speed of light, frequency, and wavelength.

Step-by-step explanation:

To calculate the wavelength (λ) of X-rays in air given their frequency (f), we use the formula λ = c / f, where c is the speed of light in air (approximately 3.00 × 10^8 m/s). For X-rays with a frequency of 1.0 × 10^19 Hz, the wavelength would be λ = 3.00 × 10^8 m/s / 1.0 × 1019 Hz. Upon performing the division, we find that the wavelength of these X-rays in air is 3.00 × 10^-11 m, which can be converted into nanometers (nm) by multiplying by 10^9 nm/m, resulting in 0.03 nm.

Answer 2

For any electromagnetic wave, the relationship between frequency and wavelength is given by

`\lambda = (c)/(f)`
where

`\lambda` is the wavelength
c is the speed of light (the speed of the electromagnetic wave)
f is the frequency

For the X-rays in our problem, the frequency is
`f=1.0 \cdot 10^(19)Hz`, while the speed of light is
`c=3.0 \cdot 10^8 m/s`, so the wavelength of this radiation is

`\lambda= (3 \cdot 10^8 m/s)/(1.0 \cdot 10^(19) Hz) =3 \cdot 10^(-11) m`