What is the wavelength of a photon of energy 1 eV?

Options

A. `12.4xx10^(3) A`
B. `2.4xx10^(3) A`
C. `0.4xx10^(2) A`
D. `1000A`

Explanation

To find the wavelength of a photon with energy of 1 eV, we can use the formula that relates the energy of a photon to its wavelength:

### Step 1: Write the formula for the energy of a photon
The energy \( E \) of a photon is given by the equation:
\[ E = \frac{hc}{\lambda} \]
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 (\( 3 \times 10^{8} \, \text{m/s} \)),
- \( \lambda \) is the wavelength of the photon.

### Step 2: Rearrange the formula to solve for wavelength
To find the wavelength \( \lambda \), we can rearrange the formula:
\[ \lambda = \frac{hc}{E} \]

### Step 3: Convert energy from eV to Joules
We know that \( 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} \). Therefore, the energy \( E \) in joules is:
\[ E = 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} \]

### Step 4: Substitute the values into the wavelength formula
Now, substituting the values of \( h \), \( c \), and \( E \) into the wavelength formula:
\[ \lambda = \frac{(6.626 \times 10^{-34} \, \text{J s})(3 \times 10^{8} \, \text{m/s})}{1.6 \times 10^{-19} \, \text{J}} \]

### Step 5: Calculate the numerator
Calculating the numerator:
\[ 6.626 \times 10^{-34} \times 3 \times 10^{8} = 1.9878 \times 10^{-25} \, \text{J m} \]

### Step 6: Calculate the wavelength
Now, divide by the energy:
\[ \lambda = \frac{1.9878 \times 10^{-25}}{1.6 \times 10^{-19}} = 1.241125 \times 10^{-6} \, \text{m} \]

### Step 7: Convert meters to angstroms
Since \( 1 \, \text{angstrom} = 10^{-10} \, \text{m} \), we convert the wavelength to angstroms:
\[ \lambda = 1.241125 \times 10^{-6} \, \text{m} = 124.1125 \times 10^{3} \, \text{angstroms} = 1241.125 \, \text{angstroms} \]

### Final Answer
Thus, the wavelength of a photon with energy of 1 eV is approximately:
\[ \lambda \approx 1241.125 \, \text{angstroms} \]

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