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 (angstrom), we can follow these steps:

### Step 1: Convert Wavelength to Meters
The given wavelength is in angstroms. We need to convert it to meters for standard calculations.

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

### Step 2: Use the Energy-Wavelength Relationship
The energy \( E \) of a photon can be calculated using 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 in meters.

### Step 3: Substitute the Values into the Formula
Now, we can substitute the values into the formula:

\[ E = \frac{(6.626 \times 10^{-34} \, \text{J s}) \times (3.00 \times 10^{8} \, \text{m/s})}{0.50 \times 10^{-10} \, \text{m}} \]

### Step 4: Calculate the Energy
Now, we perform the calculation:

\[ E = \frac{(6.626 \times 10^{-34}) \times (3.00 \times 10^{8})}{0.50 \times 10^{-10}} \]

Calculating the numerator:

\[ 6.626 \times 3.00 = 19.878 \times 10^{-34 + 8} = 19.878 \times 10^{-26} \]

Now, divide by \( 0.50 \times 10^{-10} \):

\[ E = \frac{19.878 \times 10^{-26}}{0.50 \times 10^{-10}} = 39.756 \times 10^{-16} \, \text{J} \]

This simplifies to:

\[ E = 3.9756 \times 10^{-15} \, \text{J} \]

### Step 5: Final Answer
Rounding this to three significant figures gives us:

\[ E \approx 3.98 \times 10^{-15} \, \text{J} \]

Thus, the energy of the photon corresponding to a wavelength of 0.50 Å is approximately \( 3.98 \times 10^{-15} \, \text{J} \).

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