What is the energy in joule of photon of light whose wave length is 1.0 x` 10^5 `nm

Options

A. 1.9 x `10^(-21)`
B. 1.5 x `10^(-19)`
C. 3.5 x `10^(-20)`
D. 4.5 x `10^(-19)`

Explanation

To find the energy of a photon of light with a given wavelength, 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 in meters.

### Step 1: Convert the wavelength from nanometers to meters
Given wavelength \( \lambda = 1.0 \times 10^5 \, \text{nm} \).

To convert nanometers to meters, use the conversion factor \( 1 \, \text{nm} = 1 \times 10^{-9} \, \text{m} \):

\[ \lambda = 1.0 \times 10^5 \, \text{nm} \times 1 \times 10^{-9} \, \text{m/nm} = 1.0 \times 10^{-4} \, \text{m} \]

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

\[ E = \frac{(6.626 \times 10^{-34} \, \text{J s}) \times (3.00 \times 10^{8} \, \text{m/s})}{1.0 \times 10^{-4} \, \text{m}} \]

### Step 3: Calculate the energy
Calculating the numerator:

\[ 6.626 \times 10^{-34} \times 3.00 \times 10^{8} = 1.9878 \times 10^{-25} \, \text{J m} \]

Now, divide by the wavelength:

\[ E = \frac{1.9878 \times 10^{-25} \, \text{J m}}{1.0 \times 10^{-4} \, \text{m}} = 1.9878 \times 10^{-21} \, \text{J} \]

### Step 4: Round the answer
Rounding this value gives us:

\[ E \approx 1.99 \times 10^{-21} \, \text{J} \]

### Final Answer
The energy of the photon is approximately \( 1.99 \times 10^{-21} \, \text{J} \).

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