A hypothetical electromagnetic wave is show below.
The frequency of the wave is x × 10¹⁹ Hz.
x= _________ (nearest integer)

Solution

Chemistry ma’am · 3 steps

Crest to the next zero crossing is only a quarter of a wave, so multiply 1.5 pm by 4 first.

1. Read the figure. The marked distance runs from a crest to the point where the wave next crosses the axis. One full wave goes crest, zero, trough, zero, crest, so this gap is 1/4 of a wavelength.
2. Full wavelength. λ = 4 × 1.5 pm = 6 pm = 6 × 10⁻¹² m.

   ν = c/λ = (3 × 10⁸ m s⁻¹)/(6 × 10⁻¹² m) = 5 × 10¹⁹ Hz

3. So. The frequency is 5 × 10¹⁹ Hz, so x = 5.

The common slip: 20. Taking 1.5 pm as the full wavelength gives ν = 2 × 10²⁰ Hz, so x = 20. The marked gap is only a quarter of a wave.

The idea to keep. Before using ν = c/λ, check what part of the wave the figure marks: crest to crest is λ, crest to trough is λ/2, crest to the next zero crossing is λ/4.

Answer from the NTA final answer key. Solution by PrepWiser.