What will be the energy of a photon which corresponds to the wavelength of 0.50 Å?

Options

A. `3.98xx10^(-15)J`
B. `3xx10^(15)J`
C. `3.9xx10^(8)J`
D. `3xx10^(-34)J`

Explanation

To find the energy of a photon corresponding to a wavelength of 0.50 Å, we can use the formula:

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

Where:
- \( E \) is the energy of the photon,
- \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \) Joule seconds),
- \( c \) is the speed of light (\( 3 \times 10^{8} \) meters per second),
- \( \lambda \) is the wavelength in meters.

### Step 1: Convert the wavelength from angstroms to meters
Given that \( 1 \, \text{Å} = 10^{-10} \, \text{m} \), we convert \( 0.50 \, \text{Å} \) to meters:

\[ \lambda = 0.50 \, \text{Å} = 0.50 \times 10^{-10} \, \text{m} = 5.0 \times 10^{-11} \, \text{m} \]

### Step 2: Substitute the values into the energy formula
Now we can substitute the values of \( h \), \( c \), and \( \lambda \) into the energy formula:

\[ E = \frac{(6.626 \times 10^{-34} \, \text{J s}) \times (3 \times 10^{8} \, \text{m/s})}{5.0 \times 10^{-11} \, \text{m}} \]

### Step 3: Calculate the numerator
First, calculate the numerator:

\[ 6.626 \times 10^{-34} \times 3 \times 10^{8} = 1.9878 \times 10^{-25} \, \text{J m} \]

### Step 4: Divide by the wavelength
Now, divide the result from the numerator by the wavelength:

\[ E = \frac{1.9878 \times 10^{-25} \, \text{J m}}{5.0 \times 10^{-11} \, \text{m}} = 3.9756 \times 10^{-15} \, \text{J} \]

### Step 5: Round the answer
We can round this to:

\[ E \approx 3.976 \times 10^{-15} \, \text{J} \]

### Final Answer
The energy of the photon corresponding to a wavelength of 0.50 Å is approximately:

\[ E \approx 3.976 \times 10^{-15} \, \text{J} \]

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