A photon has momentum of magnitude `8.24xx10^(-28) kg-m//s`. (a) What is the energy of this photon? Given your answer in joules and in electron volts
(b) What is the wavelength of this photon? In what region of the electormagnetic spectrum does lie?

Explanation

To solve the problem step by step, we will break it down into two parts as specified in the question.

### Part (a): Calculate the Energy of the Photon

1. **Identify the given values**:
- Momentum (P) of the photon: \( P = 8.24 \times 10^{-28} \, \text{kg m/s} \)
- Speed of light (c): \( c = 3 \times 10^{8} \, \text{m/s} \)

2. **Use the formula for energy**:
The energy (E) of a photon can be calculated using the formula:
\[ E = P \cdot c \]

3. **Substitute the values into the formula**:
\[ E = (8.24 \times 10^{-28} \, \text{kg m/s}) \cdot (3 \times 10^{8} \, \text{m/s}) \]

4. **Perform the multiplication**:
- Calculate the numerical part: \( 8.24 \times 3 = 24.72 \)
- Calculate the powers of ten: \( 10^{-28} \times 10^{8} = 10^{-20} \)
- Combine the results:
\[ E = 24.72 \times 10^{-20} \, \text{J} = 2.472 \times 10^{-19} \, \text{J} \]

5. **Convert energy from joules to electron volts**:
To convert joules to electron volts, use the conversion factor \( 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} \):
\[ E = \frac{2.472 \times 10^{-19} \, \text{J}}{1.6 \times 10^{-19} \, \text{J/eV}} \approx 1.545 \, \text{eV} \]

### Summary of Part (a):
- Energy in joules: \( 2.472 \times 10^{-19} \, \text{J} \)
- Energy in electron volts: \( 1.545 \, \text{eV} \)

---

### Part (b): Calculate the Wavelength of the Photon

1. **Identify the given values**:
- Planck's constant (h): \( h = 6.626 \times 10^{-34} \, \text{J s} \)
- Momentum (P): \( P = 8.24 \times 10^{-28} \, \text{kg m/s} \)

2. **Use the formula for wavelength**:
The wavelength (\( \lambda \)) of a photon can be calculated using the formula:
\[ \lambda = \frac{h}{P} \]

3. **Substitute the values into the formula**:
\[ \lambda = \frac{6.626 \times 10^{-34} \, \text{J s}}{8.24 \times 10^{-28} \, \text{kg m/s}} \]

4. **Perform the division**:
- Calculate the numerical part: \( \frac{6.626}{8.24} \approx 0.805 \)
- Calculate the powers of ten: \( 10^{-34} \div 10^{-28} = 10^{-6} \)
- Combine the results:
\[ \lambda \approx 0.805 \times 10^{-6} \, \text{m} = 8.05 \times 10^{-7} \, \text{m} = 805 \, \text{nm} \]

5. **Determine the region of the electromagnetic spectrum**:
The wavelength of \( 805 \, \text{nm} \) lies in the infrared (IR) region of the electromagnetic spectrum.

### Summary of Part (b):
- Wavelength: \( 805 \, \text{nm} \)
- Region of the electromagnetic spectrum: Infrared (IR)

---