Frequency of a wave is `6 xx 10^(15)` Hz. The wave is

Options

A. ` 10 ^(5) cm^(-1)`
B. ` 2xx 10 ^(7) m^(-1)`
C. `2 xx 10 ^(7) cm ^(-1)`
D. `2 xx 10 ^(5) m^(-1)`

Answer

To determine the nature of the wave with a frequency of \(6 \times 10^{15}\) Hz, we can follow these steps:

### Step 1: Understand the relationship between frequency, wavelength, and the speed of light.
The relationship between frequency (\( \nu \)), wavelength (\( \lambda \)), and the speed of light (\( c \)) is given by the equation:
\[ \nu = \frac{c}{\lambda} \]
where:
- \( \nu \) is the frequency in hertz (Hz),
- \( c \) is the speed of light in vacuum, approximately \(3 \times 10^8\) meters per second,
- \( \lambda \) is the wavelength in meters.

### Step 2: Rearrange the formula to find the wavelength.
From the equation, we can rearrange it to find the wavelength:
\[ \lambda = \frac{c}{\nu} \]

### Step 3: Substitute the known values into the equation.
Substituting the values of \(c\) and \(\nu\):
\[ \lambda = \frac{3 \times 10^8 \text{ m/s}}{6 \times 10^{15} \text{ Hz}} \]

### Step 4: Calculate the wavelength.
Now, we perform the calculation:
\[ \lambda = \frac{3 \times 10^8}{6 \times 10^{15}} = \frac{3}{6} \times 10^{8 - 15} = 0.5 \times 10^{-7} \text{ m} = 5 \times 10^{-8} \text{ m} \]

### Step 5: Determine the type of wave.
The wavelength \(5 \times 10^{-8}\) meters (or 50 nm) falls within the electromagnetic spectrum, specifically in the ultraviolet (UV) range. Waves in this range are often associated with high energy and are capable of causing ionization.

### Conclusion:
Thus, the wave with a frequency of \(6 \times 10^{15}\) Hz is an ultraviolet wave.

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