25. 25.1 Give the equation (formula) that is used to calculate the energy of a photon. 25.1 in terms of $$ h $$ and $$ f $$ : 25.2 interms of $$ h $$, cand $$ \lambda $$ : $$ \qquad $$ 25.3 What is the name, value and unit of the prowortionality constant c in the above equations? $$ \qquad $$ 26. Why will an infrared photon have less e.aetav then ar ultreviolet ohoton? $$ \qquad $$ $$ \qquad $$ 27. Why will the photon of red light have less penemation abiity than a gamma ray photon? $$ \qquad $$

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### 25.1 Energy of a Photon in Terms of $$ h $$ and $$ f $$

The energy $$ E $$ of a photon can be calculated using the formula:
$$
E = h \cdot f
$$
where:
- $$ E $$ is the energy of the photon,
- $$ h $$ is Planck's constant,
- $$ f $$ is the frequency of the photon.

### 25.2 Energy of a Photon in Terms of $$ h $$, $$ c $$, and $$ \lambda $$

The energy of a photon can also be expressed in terms of its wavelength $$ \lambda $$ using the relationship between frequency, wavelength, and the speed of light $$ c $$:
$$
E = \frac{h \cdot c}{\lambda}
$$
where:
- $$ c $$ is the speed of light,
- $$ \lambda $$ is the wavelength of the photon.

### 25.3 Proportionality Constant $$ c $$

The proportionality constant $$ c $$ is known as the speed of light in a vacuum. Its value is:
$$
c \approx 3.00 \times 10^8 \, \text{m/s}
$$
The unit of $$ c $$ is meters per second (m/s).

### 26. Infrared Photon vs. Ultraviolet Photon

An infrared photon has less energy than an ultraviolet photon because of their respective frequencies. The energy of a photon is directly proportional to its frequency ($$ E = h \cdot f $$). Infrared light has a lower frequency than ultraviolet light, which means that infrared photons carry less energy.

### 27. Red Light Photon vs. Gamma Ray Photon

A photon of red light has less penetration ability than a gamma ray photon due to the differences in energy and wavelength. Gamma rays have much higher energy and shorter wavelengths compared to red light. Higher energy photons (like gamma rays) can penetrate materials more effectively than lower energy photons (like red light) because they can interact with matter in a way that allows them to pass through without being absorbed or scattered as easily.

In summary:
- Infrared photons have lower energy than ultraviolet photons due to lower frequency.
- Red light photons have less penetration ability than gamma rays due to lower energy and longer wavelength.
- **Photon Energy Formulas:** - $$ E = h \cdot f $$ (energy in terms of Planck's constant $$ h $$ and frequency $$ f $$) - $$ E = \frac{h \cdot c}{\lambda} $$ (energy in terms of $$ h $$, speed of light $$ c $$, and wavelength $$ \lambda $$) - **Proportionality Constant $$ c $$:** - **Name:** Speed of light in a vacuum - **Value:** Approximately $$ 3.00 \times 10^8 \, \text{m/s} $$ - **Unit:** Meters per second (m/s) - **Energy Comparisons:** - **Infrared vs. Ultraviolet Photons:** Infrared photons have less energy than ultraviolet photons because infrared light has a lower frequency. - **Red Light vs. Gamma Rays:** Red light photons have less penetration ability than gamma rays because gamma rays have higher energy and shorter wavelengths, allowing them to pass through materials more effectively.

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