Question

What is the wavelength of radiation that has a frequency of 5.39 × 10¹⁴ s⁻¹?

(c-2.9979 x 10⁸ m/s)
A) 618 nm
B) 1.80 × 10⁻³ nm
C) 6180 nm
D) 1.61 × 10²³ nm
E) 556 nm

Answer 1

To calculate the wavelength of radiation with a frequency of 5.39 × 10¹⁴ s⁻¹, use the formula λ = c / f. Substituting the given values yields a wavelength (λ) of 556 nm, so the correct answer is E) 556 nm.

Step-by-step explanation:

To find the wavelength of radiation with a given frequency, you can use the formula:

c = λf

where:

• c is the speed of light (2.9979 × 10⁸ m/s),
• λ is the wavelength,
• f is the frequency.

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

λ = c / f

Substitute the given frequency (5.39 × 10¹⁴ s⁻¹) into the formula:

λ = (2.9979 × 10⁸ m/s) / (5.39 × 10¹⁴ s⁻¹)

Performing the division gives the wavelength λ in meters. To convert meters to nanometers (nm), multiply by 10⁹ nm/m since 1 nm = 1 × 10⁻¹ m.

Let's calculate:

λ = (2.9979 × 10⁸ m/s) / (5.39 × 10¹⁴ s⁻¹)

λ = 5.56 × 10⁻· m = 556 nm

Therefore, the correct answer is E) 556 nm.