The energy of a photon of wavelength 390 nm is nearly

Options

A. 6.6 eV
B. 3.2 eV
C. 5.5 eV
D. 1.2 eV

Explanation

To find the energy of a photon with a wavelength of 390 nm, we can use the formula that relates the energy of a photon to its wavelength:

### Step 1: Understand the relationship between energy and wavelength
The energy \( E \) of a photon is given by the equation:
\[ E = \frac{hc}{\lambda} \]
where:
- \( E \) is the energy of the photon,
- \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \, \text{Js} \)),
- \( c \) is the speed of light (\( 3 \times 10^8 \, \text{m/s} \)),
- \( \lambda \) is the wavelength of the photon in meters.

### Step 2: Convert the wavelength from nanometers to meters
Given the wavelength \( \lambda = 390 \, \text{nm} \):
\[ \lambda = 390 \times 10^{-9} \, \text{m} \]

### Step 3: Substitute the values into the energy formula
Now we can substitute the values of \( h \), \( c \), and \( \lambda \) into the energy equation:
\[ E = \frac{(6.626 \times 10^{-34} \, \text{Js}) \times (3 \times 10^8 \, \text{m/s})}{390 \times 10^{-9} \, \text{m}} \]

### Step 4: Calculate the energy in joules
Calculating the numerator:
\[ E = \frac{1.9878 \times 10^{-25} \, \text{Js}}{390 \times 10^{-9} \, \text{m}} = 5.09 \times 10^{-19} \, \text{J} \]

### Step 5: Convert the energy from joules to electronvolts
To convert joules to electronvolts, we use the conversion factor \( 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} \):
\[ E = \frac{5.09 \times 10^{-19} \, \text{J}}{1.6 \times 10^{-19} \, \text{J/eV}} \approx 3.18 \, \text{eV} \]

### Step 6: Round to the nearest option
The closest answer to our calculation is approximately \( 3.2 \, \text{eV} \).

### Final Answer
The energy of a photon of wavelength 390 nm is nearly **3.2 eV**.

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