The mass of a photon with a wavelength equal to `1.54 xx 10^-8 cm` is.

Options

A. `0.8268 xx 10^-34 kg`
B. `1.2876 xx 10^-33 kg`
C. `1.4285 xx 10^-32 kg`
D. `1.8884 xx 10^-32 kg`

Explanation

To find the mass of a photon with a given wavelength, we can use the relationship between wavelength, mass, and the speed of light. Here are the steps to solve the problem:

### Step 1: Convert Wavelength to Meters
The given wavelength is \(1.54 \times 10^{-8} \text{ cm}\). We need to convert this into meters:
\[ 1 \text{ cm} = 0.01 \text{ m} \]
Thus,
\[ 1.54 \times 10^{-8} \text{ cm} = 1.54 \times 10^{-8} \times 0.01 \text{ m} = 1.54 \times 10^{-10} \text{ m} \]

### Step 2: Use the Photon Wavelength Formula
The wavelength (\(\lambda\)) of a photon is related to its mass (m) and the speed of light (c) by the equation:
\[ \lambda = \frac{h}{mv} \]
Where:
- \(h\) is Planck's constant (\(6.626 \times 10^{-34} \text{ J s}\))
- \(v\) is the speed of light (\(c = 3 \times 10^{8} \text{ m/s}\))

### Step 3: Rearrange the Formula to Solve for Mass
Rearranging the formula to solve for mass (m):
\[ m = \frac{h}{\lambda v} \]

### Step 4: Substitute the Values
Now substitute the values into the equation:
\[ m = \frac{6.626 \times 10^{-34} \text{ J s}}{(1.54 \times 10^{-10} \text{ m})(3 \times 10^{8} \text{ m/s})} \]

### Step 5: Calculate the Mass
Calculating the denominator:
\[ 1.54 \times 10^{-10} \text{ m} \times 3 \times 10^{8} \text{ m/s} = 4.62 \times 10^{-2} \text{ m}^2/\text{s} \]
Now substituting back into the mass equation:
\[ m = \frac{6.626 \times 10^{-34}}{4.62 \times 10^{-2}} \approx 1.43 \times 10^{-32} \text{ kg} \]

### Final Answer
The mass of the photon is approximately:
\[ m \approx 1.43 \times 10^{-32} \text{ kg} \]