What is the frequency of light wave whose time period is `2.0 xx10^(10)` sec

Options

A. `5xx10^(9)` s
B. `4 xx10^(9)` s
C. `5xx10^(-11) s^(-1)`
D. `4xx10^(9) s^(-1)`

Answer

To find the frequency of a light wave given its time period, we can use the formula:

\[ \text{Frequency} (f) = \frac{1}{\text{Time Period} (T)} \]

### Step-by-Step Solution:

1. **Identify the Time Period**:
The time period \( T \) is given as \( 2.0 \times 10^{10} \) seconds.

2. **Apply the Frequency Formula**:
Substitute the value of the time period into the frequency formula:
\[ f = \frac{1}{T} = \frac{1}{2.0 \times 10^{10}} \]

3. **Calculate the Frequency**:
To calculate the frequency, we can simplify:
\[ f = \frac{1}{2.0} \times \frac{1}{10^{10}} = 0.5 \times 10^{-10} \]

4. **Adjust the Scientific Notation**:
To express \( 0.5 \) in scientific notation, we can write it as \( 5.0 \times 10^{-1} \):
\[ f = 5.0 \times 10^{-1} \times 10^{-10} = 5.0 \times 10^{-11} \]

5. **Final Result**:
Therefore, the frequency of the light wave is:
\[ f = 5.0 \times 10^{-11} \text{ Hz} \]

### Summary:
The frequency of the light wave whose time period is \( 2.0 \times 10^{10} \) seconds is \( 5.0 \times 10^{-11} \) Hz.

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