The energy of a photon is given as `3.03xx10^(-19)J`. The wavelength of the photon is

Options

A. 6.56 nm
B. 65.6 nm
C. 0.656 nm
D. 656 nm

Explanation

To find the wavelength of a photon given its energy, we can use the formula:

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

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

We can rearrange this formula to solve for wavelength (\( \lambda \)):

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

Now, let's substitute the known values into the equation.

### Step 1: Identify the values
- \( h = 6.626 \times 10^{-34} \, \text{J s} \)
- \( c = 3.00 \times 10^{8} \, \text{m/s} \)
- \( E = 3.03 \times 10^{-19} \, \text{J} \)

### Step 2: Substitute the values into the equation
\[ \lambda = \frac{(6.626 \times 10^{-34} \, \text{J s}) \times (3.00 \times 10^{8} \, \text{m/s})}{3.03 \times 10^{-19} \, \text{J}} \]

### Step 3: Calculate the numerator
First, calculate \( h \times c \):
\[ h \times c = 6.626 \times 10^{-34} \times 3.00 \times 10^{8} \]
\[ = 1.9878 \times 10^{-25} \, \text{J m} \]

### Step 4: Calculate the wavelength
Now, substitute this value into the equation:
\[ \lambda = \frac{1.9878 \times 10^{-25} \, \text{J m}}{3.03 \times 10^{-19} \, \text{J}} \]
\[ = 6.56 \times 10^{-7} \, \text{m} \]

### Step 5: Convert to nanometers
To convert meters to nanometers:
\[ \lambda = 6.56 \times 10^{-7} \, \text{m} = 656 \, \text{nm} \]

### Final Answer:
The wavelength of the photon is \( 656 \, \text{nm} \).

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