An emission ray has a frequency of 5.10 × 10¹ê hz. given that the speed of light is 2.998 × 10§ m/s, what is the wavelength of the ray?

The answer is 5.88 · 10⁻⁷ m.

To calculate this we will use the light equation:

v = λ · f,
where:
v - the speed of light (units: m/s)
λ - the wavelength of the ray (units: m)
f - the frequency of the ray (units: Hz = 1/s since Hz means cycles per second (f=1/T))

It is given:
f = 5.10 · 10¹⁴ Hz = 5.10 · 10¹⁴ 1/s
v = 2.998 · 10⁸ m/s
λ = ?

If v = λ · f, then λ = v ÷ f:
λ = 2.998 · 10⁸ m/s ÷ 5.10 · 10¹⁴ 1/s
   = 0.588 · 10⁸⁻¹⁴ · m
   = 0.588 · 10⁻⁶ m
   = 5.88 · 10⁻⁷ m

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