Question

What is the frequency f in Hz of light that has wavelength 157 nm?

1 eV = 1.602 ✕ 10⁻¹⁹ J,
e = 1.602 ✕ 10⁻¹⁹ C,
c = 2.998 ✕ 10⁸ m/s,
and
h = 6.626 ✕ 10⁻³⁴ J · s = 4.136 ✕ 10⁻¹⁵ eV · s
(Use as necessary.)

Answer 1

The frequency of light with a wavelength of 157 nm is approximately 1.91 × 10·⁷ Hz, calculated using the relationship c = λf, where c is the speed of light and λ is the wavelength.

Step-by-step explanation:

To find the frequency (f) in Hertz (Hz) of light with a given wavelength (λ), we use the fundamental relationship between the speed of light (c), wavelength (λ), and frequency (f), which is c = λf. Here, c is the speed of light with a value of 2.998 × 10⁸ m/s, and λ is the wavelength of light in meters.

If the wavelength (λ) of light is 157 nm (1 nm = 1 × 10⁼⁹ m), we first need to convert this wavelength into meters by multiplying by 10⁼⁹. So, λ = 157 nm = 157 × 10⁼⁹ m.

Now, rearranging the formula to solve for frequency (f), we get f = c / λ. Substituting the values in gives us:

f = (2.998 × 10⁸ m/s) / (157 × 10⁼⁹ m) = 1.91 × 10·⁷ Hz

Therefore, the frequency of light that has a wavelength of 157 nm is approximately 1.91 × 10·⁷ Hz.