The energy of a 700- nm photon is :-

Options

A. 1.77 eV
B. 2.47 eV
C. 700 eV
D. 3.57 eV

Answer

To find the energy of a 700-nm photon, we can follow these steps:

### Step 1: Convert Wavelength to Meters
The given wavelength is 700 nm (nanometers). We need to convert this to meters for our calculations.

\[ \text{Wavelength in meters} = 700 \, \text{nm} = 700 \times 10^{-9} \, \text{m} = 7 \times 10^{-7} \, \text{m} \]

### Step 2: Use the Energy Formula
The energy \( E \) of a photon can be calculated using the formula:

\[ E = h \nu \]

where \( h \) is Planck's constant and \( \nu \) (nu) is the frequency of the photon. The frequency can be calculated using the speed of light \( c \) and the wavelength \( \lambda \):

\[ \nu = \frac{c}{\lambda} \]

### Step 3: Substitute Values
Planck's constant \( h \) is \( 6.626 \times 10^{-34} \, \text{J s} \) and the speed of light \( c \) is \( 3 \times 10^{8} \, \text{m/s} \). Now substitute the values into the frequency formula:

\[ \nu = \frac{3 \times 10^{8} \, \text{m/s}}{7 \times 10^{-7} \, \text{m}} \]

### Step 4: Calculate Frequency
Now, calculate the frequency:

\[ \nu = \frac{3 \times 10^{8}}{7 \times 10^{-7}} \approx 4.29 \times 10^{14} \, \text{Hz} \]

### Step 5: Calculate Energy in Joules
Now substitute the frequency back into the energy formula:

\[ E = h \nu = 6.626 \times 10^{-34} \, \text{J s} \times 4.29 \times 10^{14} \, \text{Hz} \]

Calculating this gives:

\[ E \approx 2.85 \times 10^{-19} \, \text{J} \]

### Step 6: Convert Energy to Electron Volts
To convert the energy from Joules to electron volts, we use the conversion factor \( 1 \, \text{eV} = 1.602 \times 10^{-19} \, \text{J} \):

\[ E \, (\text{in eV}) = \frac{2.85 \times 10^{-19} \, \text{J}}{1.602 \times 10^{-19} \, \text{J/eV}} \approx 1.78 \, \text{eV} \]

### Final Answer
The energy of a 700-nm photon is approximately **1.78 eV**.

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