If the velocity of light in free space is `3xx10^(8)` m/s , then value of wavelength of electromagnetic wave of frequency `2xx10^(6)` Hz will be

Options

A. `6xx10^(8)` m
B. `15xx10^(4)` m
C. 150 m
D. `1.5xx10^(11)` m

Answer

To find the wavelength of an electromagnetic wave given its frequency, we can use the formula:

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

where:
- \(\lambda\) is the wavelength,
- \(C\) is the speed of light in free space (\(3 \times 10^8\) m/s),
- \(\nu\) is the frequency of the wave (\(2 \times 10^6\) Hz).

Now, let's calculate the wavelength step by step.

### Step 1: Write down the formula for wavelength
The formula to calculate the wavelength (\(\lambda\)) is:

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

### Step 2: Substitute the values into the formula
Substituting the given values into the formula:

\[ \lambda = \frac{3 \times 10^8 \, \text{m/s}}{2 \times 10^6 \, \text{Hz}} \]

### Step 3: Simplify the expression
Now, we can simplify the fraction:

\[ \lambda = \frac{3}{2} \times \frac{10^8}{10^6} \]

### Step 4: Calculate the powers of ten
Using the properties of exponents, we can simplify \( \frac{10^8}{10^6} \):

\[ \frac{10^8}{10^6} = 10^{8-6} = 10^2 \]

### Step 5: Calculate the numerical part
Now, we can calculate the numerical part:

\[ \frac{3}{2} = 1.5 \]

### Step 6: Combine the results
Now, we combine the results:

\[ \lambda = 1.5 \times 10^2 \, \text{m} \]

### Step 7: Final result
Thus, the wavelength is:

\[ \lambda = 150 \, \text{m} \]

### Final Answer
The value of the wavelength of the electromagnetic wave is **150 meters**.

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