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The value of Planck’s constant is 6.63 × 10⁻³⁴ Js. The velocity of light is 3.0 × 10⁸ m s⁻¹. Which value is closest to the wavelength in nanometers of a quantum of light with frequency of 8 × 10¹⁵ s⁻¹?
- 3 × 10⁷
- 2 × 10⁵
- 5 × 10⁸
- 4 × 10¹
Correct answer: 4 × 10¹
Solution
The wavelength (λ) is calculated using the formula λ = c / ν, where c is the speed of light and ν is the frequency. Substituting c = 3.0 × 10⁸ m/s and ν = 8 × 10¹⁵ s⁻¹, we get λ = (3.0 × 10⁸) / (8 × 10¹⁵) = 3.75 × 10⁻⁸ m = 37.5 nm, which is closest to 4 × 10¹ nm.
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