The value of Planck's constant is 6.63 × 10⁻³⁴ Js. The speed of light is 3 × 10¹⁷ nm s⁻¹. Which value is close

Question

The value of Planck's constant is 6.63 × 10⁻³⁴ Js. The speed of light is 3 × 10¹⁷ nm s⁻¹. Which value is closest to the wavelength in nanometers of a quantum of light with a frequency of 6 × 10¹⁵ s⁻¹?

Accepted Answer

The relationship between the speed of light ($c$), frequency ($
u$), and wavelength ($\lambda$) is given by the wave equation :
$$ c = 
u \lambda $$

To find the wavelength ($\lambda$), we rearrange the formula:
$$ \lambda = \frac{c}{
u} $$

**Given values:**
*   Speed of light ($c$) = $3 	imes 10^{17} 	ext{ nm s}^{-1}$
*   Frequency ($
u$) = $6 	imes 10^{15} 	ext{ s}^{-1}$

**Calculation:**
$$ \lambda = \frac{3 	imes 10^{17}}{6 	imes 10^{15}} $$
$$ \lambda = 0.5 	imes 10^{2} 	ext{ nm} $$
$$ \lambda = 50 	ext{ nm} $$

(Note: Planck's constant is provided as distractor data and is not required for calculating wavelength from frequency and speed).

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