The energy of light of frequency 2.0 x 10$^{15}$Hz is  (h = 6.63 x 10$^{-34}$Js)

Analyze the question: We need the energy of a photon of light with a given frequency. This is a quantum physics (Planck's equation) question.

Concept: The energy of a photon is given by Planck's equation:

E = hf

where

• h = Planck's constant = 6.63 × 10⁻³⁴ Js
• f = frequency = 2.0 × 10¹⁵ Hz

Solution:

E = (6.63 × 10⁻³⁴) × (2.0 × 10¹⁵)

Multiply the numbers: 6.63 × 2.0 = 13.26

Add the powers of 10: 10⁻³⁴ × 10¹⁵ = 10⁻¹⁹

E = 13.26 × 10⁻¹⁹ J

Convert to standard form: 13.26 × 10⁻¹⁹ = 1.326 × 10⁻¹⁸ J

E ≈ 1.33 × 10⁻¹⁸ J

Tip: When multiplying in standard form, handle the numbers and the powers of 10 separately. Then check that your final answer has only one non-zero digit before the decimal point. Here, 13.26 × 10⁻¹⁹ had to become 1.326 × 10⁻¹⁸. Forgetting this step is how you would end up picking option C by mistake. Also remember that a frequency of order 10¹⁵ Hz (ultraviolet) typically gives photon energies of order 10⁻¹⁸ J.