For a photon having wavelength `2000Å`, calculate
a. wave number
b. frequency.

Answer

To solve the problem of calculating the wave number and frequency for a photon with a wavelength of 2000 Å, we will follow these steps:

### Step 1: Convert Wavelength to Meters
The given wavelength is in angstroms (Å). We need to convert it to meters because standard SI units are required for calculations.

1 Å = \(10^{-10}\) meters

So,
\[ \text{Wavelength} (\lambda) = 2000 \, \text{Å} = 2000 \times 10^{-10} \, \text{m} = 2.0 \times 10^{-7} \, \text{m} \]

### Step 2: Calculate Wave Number
The wave number (\( \bar{\nu} \)) is defined as the reciprocal of the wavelength. The formula is:
\[ \bar{\nu} = \frac{1}{\lambda} \]

Substituting the value of the wavelength:
\[ \bar{\nu} = \frac{1}{2.0 \times 10^{-7}} \, \text{m} = 5.0 \times 10^{6} \, \text{m}^{-1} \]

### Step 3: Calculate Frequency
The frequency (\( \nu \)) can be calculated using the speed of light (\( c \)) and the wavelength (\( \lambda \)). The formula is:
\[ \nu = \frac{c}{\lambda} \]

Where the speed of light \( c \) is approximately \( 3.0 \times 10^{8} \, \text{m/s} \).

Substituting the values:
\[ \nu = \frac{3.0 \times 10^{8} \, \text{m/s}}{2.0 \times 10^{-7} \, \text{m}} = 1.5 \times 10^{15} \, \text{Hz} \]

### Final Answers
a. Wave number: \( 5.0 \times 10^{6} \, \text{m}^{-1} \)
b. Frequency: \( 1.5 \times 10^{15} \, \text{Hz} \)

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