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Given that Planck’s constant is 6.63 × 10⁻³⁴ J s and the speed of light is 3.0 × 10⁸ m s⁻¹, which of the following is nearest to the wavelength, in nanometres, of light having frequency 8 × 10¹⁵ s⁻¹?

1. 5 × 10⁻¹⁸
2. 4 × 10¹
3. 3 × 10⁷
4. 2 × 10⁻²⁵

Correct answer: 4 × 10¹

Solution

The wavelength of light can be calculated using the formula λ = (c)/(f), where c is the speed of light and f is the frequency. Plugging in the values, we find that the wavelength corresponding to a frequency of 8 × 10¹⁵ s⁻¹ is approximately 3.75 × 10⁻⁷ m, which converts to 375 nm, closest to 4 × 10¹ nm.

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