Calculate the energy of `100` photons if the wavelength of the light is `2000 Å`.

Explanation

To calculate the energy of 100 photons with a wavelength of 2000 Å, we can follow these steps:

### Step 1: Convert the wavelength from angstroms to meters.
1 Å (angstrom) = \(10^{-10}\) meters. Therefore,
\[ \text{Wavelength} (\lambda) = 2000 \, \text{Å} = 2000 \times 10^{-10} \, \text{m} = 2.0 \times 10^{-7} \, \text{m} \]

### Step 2: Use the formula for the energy of a single photon.
The energy \(E\) of a single photon can be calculated using the formula:
\[ E = \frac{hc}{\lambda} \]
where:
- \(h\) (Planck's constant) = \(6.626 \times 10^{-34} \, \text{J s}\)
- \(c\) (speed of light) = \(3.0 \times 10^{8} \, \text{m/s}\)
- \(\lambda\) is the wavelength in meters.

### Step 3: Substitute the values into the formula.
\[ E = \frac{(6.626 \times 10^{-34} \, \text{J s})(3.0 \times 10^{8} \, \text{m/s})}{2.0 \times 10^{-7} \, \text{m}} \]

### Step 4: Calculate the energy of one photon.
Calculating the numerator:
\[ 6.626 \times 10^{-34} \times 3.0 \times 10^{8} = 1.9878 \times 10^{-25} \, \text{J m} \]
Now divide by the wavelength:
\[ E = \frac{1.9878 \times 10^{-25}}{2.0 \times 10^{-7}} = 9.939 \times 10^{-18} \, \text{J} \]

### Step 5: Calculate the total energy for 100 photons.
\[ \text{Total Energy} = 100 \times E = 100 \times 9.939 \times 10^{-18} \, \text{J} = 9.939 \times 10^{-16} \, \text{J} \]

### Step 6: Convert the energy from joules to electron volts.
To convert joules to electron volts, use the conversion factor \(1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J}\):
\[ \text{Energy in eV} = \frac{9.939 \times 10^{-16} \, \text{J}}{1.6 \times 10^{-19} \, \text{J/eV}} \approx 621.2 \, \text{eV} \]

### Final Answer:
The total energy of 100 photons with a wavelength of 2000 Å is approximately **621.2 eV**.

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