Question

Calculate the wavelength (in nm) of the red light emitted by a barcode scanner that has a frequency of 4.62 x 10¹⁴ s⁻¹. The speed of light is 3.00 x 10 ⁸ m/s and 1 nm = 10⁻⁹ m. c = λν

A) 229 nm
B) 436 nm
C) 206 nm
D) 485 nm
E) 649 nm

Answer 1

To find the wavelength of red light with a frequency of 4.62 x 10¹⁴ Hz, we use the formula c = λ
u and find that the wavelength is 649 nm.

Step-by-step explanation:

To calculate the wavelength of red light emitted by a barcode scanner, we use the relationship c = λ
u, where c is the speed of light, λ (lambda) is the wavelength, and ν (nu) is the frequency. Given that the frequency (ν) is 4.62 x 10¹⁴ Hz (s⁻¹) and the speed of light (c) is 3.00 x 10⁸ m/s, we can rearrange the equation to solve for λ: λ = c / ν. Plugging the values in, we get λ = (3.00 x 10⁸ m/s) / (4.62 x 10¹⁴ s⁻¹).

Next, calculate the result, which gives us λ = 6.49 x 10⁻⁷ meters. Since the question asks for the wavelength in nanometers (nm), we must convert meters to nanometers by recognizing that 1 m = 10⁹ nm. Therefore, λ = 6.49 x 10⁻⁷ m × 10⁹ nm/m = 649 nm.