The energy of a photon of light of wavelength 450 nm is

Options

A. `4.4 xx10^(-19) J`
B. `2.5 xx10^(-19) J`
C. `1.25 xx10^(-17) J`
D. `2.5 xx10^(-17) J`

Explanation

To find the energy of a photon of light with a wavelength of 450 nm, 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 wavelength from nanometers to meters
Given the wavelength \( \lambda = 450 \, \text{nm} \):
\[ \lambda = 450 \, \text{nm} = 450 \times 10^{-9} \, \text{m} \]

### Step 2: Substitute the values into the formula
Now, we substitute the values of \( h \), \( c \), and \( \lambda \) into the energy formula:
\[ E = \frac{(6.626 \times 10^{-34} \, \text{J s}) \times (3.00 \times 10^{8} \, \text{m/s})}{450 \times 10^{-9} \, \text{m}} \]

### Step 3: Calculate the energy
Now we perform the calculation:
1. Calculate the numerator:
\[ 6.626 \times 10^{-34} \times 3.00 \times 10^{8} = 1.9878 \times 10^{-25} \, \text{J m} \]

2. Now divide by the wavelength:
\[ E = \frac{1.9878 \times 10^{-25} \, \text{J m}}{450 \times 10^{-9} \, \text{m}} \]
\[ E = \frac{1.9878 \times 10^{-25}}{4.5 \times 10^{-7}} \]
\[ E = 4.417 \times 10^{-19} \, \text{J} \]

### Step 4: Round to significant figures
Rounding to two significant figures, we get:
\[ E \approx 4.4 \times 10^{-19} \, \text{J} \]

Thus, the energy of a photon of light with a wavelength of 450 nm is approximately \( 4.4 \times 10^{-19} \, \text{J} \).

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