The energy of a photon of light with wavelength `5000 Å` is approximately `2.5 eV`. This way the energy of an X - ray photon with wavelength `1 Å` would be

Options

A. `2.5//5000 eV`
B. `2.5//(5000)^(2) eV`
C. `2.5 xx 5000 eV`
D. `2.5 xx (5000)^(2) eV`

Explanation

To find the energy of an X-ray photon with a wavelength of 1 Å, we can use the formula for the energy of a photon:

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

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 1: Calculate \( hc \)

From the given information, we know the energy of a photon with a wavelength of \( 5000 \, \text{Å} \) is approximately \( 2.5 \, \text{eV} \). We can express this in joules since \( 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} \):

\[ E = 2.5 \, \text{eV} = 2.5 \times 1.6 \times 10^{-19} \, \text{J} = 4.0 \times 10^{-19} \, \text{J} \]

Now we can use the wavelength to find \( hc \):

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

Substituting the values:

\[ hc = 4.0 \times 10^{-19} \, \text{J} \cdot 5000 \, \text{Å} \]

Convert \( 5000 \, \text{Å} \) to meters:

\[ 5000 \, \text{Å} = 5000 \times 10^{-10} \, \text{m} = 5.0 \times 10^{-7} \, \text{m} \]

Now substituting back:

\[ hc = 4.0 \times 10^{-19} \, \text{J} \cdot 5.0 \times 10^{-7} \, \text{m} = 2.0 \times 10^{-25} \, \text{J m} \]

### Step 2: Calculate the energy of the X-ray photon

Now, we want to find the energy of a photon with a wavelength of \( 1 \, \text{Å} \):

Convert \( 1 \, \text{Å} \) to meters:

\[ 1 \, \text{Å} = 1 \times 10^{-10} \, \text{m} \]

Using the energy formula again:

\[ E = \frac{hc}{\lambda} = \frac{2.0 \times 10^{-25} \, \text{J m}}{1 \times 10^{-10} \, \text{m}} = 2.0 \times 10^{-15} \, \text{J} \]

### Step 3: Convert energy to electron volts

Now we convert the energy back to electron volts:

\[ E = \frac{2.0 \times 10^{-15} \, \text{J}}{1.6 \times 10^{-19} \, \text{J/eV}} = 1.25 \times 10^{4} \, \text{eV} = 12500 \, \text{eV} \]

### Final Answer

The energy of an X-ray photon with a wavelength of \( 1 \, \text{Å} \) is approximately \( 12500 \, \text{eV} \).

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