A photon will have less energy if its

Options

A. amplitude is higher
B. frequency is higher
C. wavelength is longer
D. wavelength is shorter

Answer

To solve the question, "A photon will have less energy if its...", we need to analyze the relationship between the energy of a photon and its frequency and wavelength.

### Step-by-Step Solution:

1. **Understanding Photon Energy**:
The energy (E) of a photon is given by the equation:
\[ E = h \nu \]
where \(h\) is Planck's constant and \(\nu\) (nu) is the frequency of the photon.

2. **Relationship Between Frequency and Wavelength**:
The speed of light (c) is related to frequency and wavelength (\(\lambda\)) by the equation:
\[ c = \nu \lambda \]
From this, we can express frequency in terms of wavelength:
\[ \nu = \frac{c}{\lambda} \]

3. **Substituting Frequency into Energy Equation**:
Substituting the expression for frequency into the energy equation gives:
\[ E = h \frac{c}{\lambda} \]
This shows that energy is inversely proportional to wavelength:
\[ E \propto \frac{1}{\lambda} \]

4. **Analyzing the Options**:
- **Amplitude is higher**: Amplitude does not affect the energy of a photon; it affects the intensity of light.
- **Frequency is higher**: Higher frequency means higher energy. This option is incorrect for less energy.
- **Wavelength is longer**: A longer wavelength means lower frequency, which results in less energy. This option is correct.
- **Wavelength is shorter**: A shorter wavelength means higher frequency, which results in more energy. This option is incorrect for less energy.

5. **Conclusion**:
The correct answer is that a photon will have less energy if its **wavelength is longer**.

### Final Answer:
The correct option is: **Wavelength is longer**.