A beam of white light is dispersed into its wavelength components of potassium metal. What of the increasing order of the velocity of the electron emitted by the different light component ?

Options

A. blue green orange yellow
B. violet blue orange red
C. yellow green blue violet
D. orange yellow blue violet

Explanation

To solve the problem of determining the increasing order of the velocity of electrons emitted by different components of white light when dispersed, we can follow these steps:

### Step 1: Understand the Composition of White Light
White light consists of a spectrum of colors, which can be separated into different wavelengths. The main colors in the spectrum are:
- Violet
- Indigo
- Blue
- Green
- Yellow
- Orange
- Red

### Step 2: Relate Wavelength to Frequency
The wavelength and frequency of light are inversely related. As the wavelength increases, the frequency decreases. The relationship can be expressed as:
\[ c = \lambda \cdot \nu \]
where:
- \( c \) is the speed of light,
- \( \lambda \) is the wavelength,
- \( \nu \) (mu) is the frequency.

### Step 3: Apply the Photoelectric Effect
According to the photoelectric effect, the kinetic energy (KE) of the emitted electrons can be expressed as:
\[ KE = \frac{1}{2} m u^2 = h \nu - \phi \]
where:
- \( m \) is the mass of the electron,
- \( u \) is the velocity of the emitted electron,
- \( h \) is Planck's constant,
- \( \nu \) is the frequency of the incident light,
- \( \phi \) is the work function of the metal (potassium in this case).

### Step 4: Determine the Relationship Between Frequency and Velocity
From the equation of kinetic energy, we can see that as the frequency \( \nu \) increases, the kinetic energy increases, which implies that the velocity \( u \) of the emitted electrons also increases. Therefore:
- Higher frequency (shorter wavelength) light will result in higher velocity of emitted electrons.
- Lower frequency (longer wavelength) light will result in lower velocity of emitted electrons.

### Step 5: Establish the Order of Colors
Given the order of colors from shortest to longest wavelength (and thus highest to lowest frequency):
1. Violet (highest frequency)
2. Indigo
3. Blue
4. Green
5. Yellow
6. Orange
7. Red (lowest frequency)

### Step 6: Write the Increasing Order of Velocity
Since the velocity of emitted electrons decreases as we move from violet to red, the increasing order of the velocity of the electrons emitted by the different light components is:
**Red < Orange < Yellow < Green < Blue < Indigo < Violet**

### Final Answer
The increasing order of the velocity of the electrons emitted by the different light components is:
**Red < Orange < Yellow < Green < Blue < Indigo < Violet**

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