Questions: A certain shade of blue has a frequency of 7.23 × 10^14 Hz. What is the energy of exactly one photon of this light? Planck's

Transcript text: A certain shade of blue has a frequency of $7.23 \times 10^{14} \mathrm{~Hz}$. What is the energy of exactly one photon of this light? Planck's \[ E= \]

Solution

Solution Steps

Step 1: Identify the Given Information

We are given the frequency of a certain shade of blue light as $7.23 \times 10^{14} \, \text{Hz}$.

Step 2: Recall the Formula for Photon Energy

The energy of a photon can be calculated using Planck's equation: \[ E = h \cdot f \] where $E$ is the energy of the photon, $h$ is Planck's constant ($6.626 \times 10^{-34} \, \text{J}\cdot\text{s}$), and $f$ is the frequency of the light.

Step 3: Substitute the Given Values into the Formula

Substitute the given frequency and Planck's constant into the formula: \[ E = (6.626 \times 10^{-34} \, \text{J}\cdot\text{s}) \cdot (7.23 \times 10^{14} \, \text{Hz}) \]

Step 4: Calculate the Energy

Perform the multiplication to find the energy: \[ E = 4.791 \times 10^{-19} \, \text{J} \]