Final answer:
The energy of a blue photon with a frequency of 7.16 × 10¹⁴ Hz can be calculated using the formula E = hf, where E is energy and h is Planck's constant. After substituting the given values and performing the calculation, the energy is found to be approximately 4.7 × 10⁻³⁹ J, which is closest to option (b) 4.8 × 10⁻³⁹ J.
Step-by-step explanation:
To calculate the energy of a photon with a frequency of 7.16 × 10¹⁴ Hz, we use the formula:
E = hf
Where:
- E is the energy of the photon.
- h is Planck's constant, which is equal to 6.626 × 10⁻³⁴ J·s.
- f is the frequency of the photon.
Substituting the given values, we get:
E = (6.626 × 10⁻³⁴ J·s) × (7.16 × 10¹⁴ Hz)
By performing the multiplication:
E = 47.42616 × 10⁻³⁴ J
Simplified, E = 4.742616 × 10⁻³⁹ J
When rounded to two significant figures (as per options given in the question), the energy of the blue photon is approximately:
E ≈ 4.7 × 10⁻³⁹ J
The closest option to this calculated value is:
(b) 4.8 × 10⁻³⁹ J