Which has a higher energy : a photon of red light with a wavelegth of `7500 Å` or a photon of green light with a wavelength of `5250 Å`?

Explanation

To determine which photon has a higher energy between a photon of red light with a wavelength of 7500 Å and a photon of green light with a wavelength of 5250 Å, we can follow these steps:

### Step 1: Understand the relationship between energy and wavelength
The energy \( E \) of a photon is inversely proportional to its wavelength \( \lambda \). This relationship can be expressed by the formula:

\[ E = \frac{hc}{\lambda} \]

where:
- \( E \) is the energy of the photon,
- \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \, \text{Js} \)),
- \( c \) is the speed of light (\( 3.00 \times 10^8 \, \text{m/s} \)),
- \( \lambda \) is the wavelength of the light.

### Step 2: Calculate the energy for both wavelengths
Since we are comparing the energies, we can use the formula \( E = \frac{hc}{\lambda} \) for both wavelengths without needing to calculate the exact energy values.

1. **For red light (7500 Å)**:
- Convert 7500 Å to meters: \( 7500 \, \text{Å} = 7500 \times 10^{-10} \, \text{m} = 7.5 \times 10^{-7} \, \text{m} \)
- Energy \( E_{red} = \frac{hc}{\lambda_{red}} = \frac{h \cdot c}{7.5 \times 10^{-7}} \)

2. **For green light (5250 Å)**:
- Convert 5250 Å to meters: \( 5250 \, \text{Å} = 5250 \times 10^{-10} \, \text{m} = 5.25 \times 10^{-7} \, \text{m} \)
- Energy \( E_{green} = \frac{hc}{\lambda_{green}} = \frac{h \cdot c}{5.25 \times 10^{-7}} \)

### Step 3: Compare the energies
Since \( E \) is inversely proportional to \( \lambda \), we can conclude that:

- The smaller the wavelength, the higher the energy.
- Comparing the wavelengths:
- Red light: \( 7500 \, \text{Å} \) (larger)
- Green light: \( 5250 \, \text{Å} \) (smaller)

### Conclusion
Since the wavelength of green light (5250 Å) is smaller than that of red light (7500 Å), the energy of the green light photon is higher.

Thus, the photon of green light has a higher energy than the photon of red light.

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