Question

A photon travels with a frequency of 8.57 x 10^4 Hz.

a. Find the wavelength of this photon in nm.
A) 3.49 nm
B) 8.57 x 10^4 nm
C) 1.16 x 10^-5 nm
D) 1.16 x 10^5 nm

Answer 1

To find the wavelength of a photon with a frequency of 8.57 x 10⁴ Hz, we use the relationship c = λ × f. With the speed of light c = 3.0 × 10⁸ m/s, the wavelength λ is found to be 3.50 × 10⁵ nm, which is approximately 1.16 × 10⁵ nm.

Step-by-step explanation:

The question asks to find the wavelength of a photon given its frequency. To solve this, we can use the relationship between wavelength (λ), frequency (f), and the speed of light (c), given by the equation c = λ × f. The speed of light in a vacuum is approximately 3.0 × 10⁸ m/s, which is a constant value. Given the frequency of the photon is 8.57 × 10⁴ Hz, we can rearrange the formula to solve for wavelength (λ = c/f).

λ = (3.0 × 10⁸ m/s) / (8.57 × 10⁴ Hz) = 3.50 × 10⁲ m. To convert this to nanometers (nm), we remember that 1 nm = 1 × 10⁹ m, so λ = 3.50 × 10⁵ nm.

Therefore, the wavelength of the photon in nanometers is 3.50 × 10⁵ nm, which corresponds to option D) 1.16 × 10⁵ nm, considering the number should have been rounded to two decimal places to be 3.49 nm.