If the frequency of violet radiation is `7.5xx10^14` Hz, then the value of wavenumber in `m^(-1)` for it is `pxx 10^5`. Give the value of p?

Answer

To find the value of the wavenumber for the given frequency of violet radiation, we can follow these steps:

### Step 1: Understand the relationship between frequency and wavenumber
The wavenumber (\( \bar{\nu} \)) is defined as the reciprocal of the wavelength (\( \lambda \)):
\[ \bar{\nu} = \frac{1}{\lambda} \]
Additionally, the relationship between frequency (\( \nu \)) and wavelength is given by:
\[ \nu = \frac{c}{\lambda} \]
where \( c \) is the speed of light.

### Step 2: Rearrange the equation to find wavenumber
From the equation of frequency, we can express wavenumber in terms of frequency:
\[ \bar{\nu} = \frac{\nu}{c} \]

### Step 3: Substitute the known values
Given:
- Frequency (\( \nu \)) = \( 7.5 \times 10^{14} \) Hz
- Speed of light (\( c \)) = \( 3 \times 10^{8} \) m/s

Substituting these values into the equation for wavenumber:
\[ \bar{\nu} = \frac{7.5 \times 10^{14}}{3 \times 10^{8}} \]

### Step 4: Perform the calculation
Calculating the right-hand side:
\[ \bar{\nu} = \frac{7.5}{3} \times \frac{10^{14}}{10^{8}} = 2.5 \times 10^{6} \text{ m}^{-1} \]

### Step 5: Express in the required format
The problem states that the wavenumber is in the form \( p \times 10^{5} \) m\(^{-1}\). We can express \( 2.5 \times 10^{6} \) as:
\[ 2.5 \times 10^{6} = 25 \times 10^{5} \]

### Step 6: Identify the value of \( p \)
From the above expression, we can see that:
\[ p = 25 \]

Thus, the final answer is:
\[ \boxed{25} \]

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