Wave length associated with electron motion

Options

A. increases with increase in the speed of electron
B. remains same irrespective of the speed of electron
C. decreases with increase of the speed of electron
D. changes with the atomic number of the atom to which it belond

Answer

To find the wavelength associated with electron motion, we can use the de Broglie wavelength formula. Here’s a step-by-step solution:

### Step 1: Understand the de Broglie wavelength formula
The de Broglie wavelength (\( \lambda \)) is given by the formula:
\[ \lambda = \frac{h}{mv} \]
where:
- \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \, \text{Js} \)),
- \( m \) is the mass of the electron,
- \( v \) is the velocity of the electron.

### Step 2: Analyze the relationship between wavelength and velocity
From the formula, we can see that the wavelength is inversely proportional to the momentum (\( mv \)):
\[ \lambda \propto \frac{1}{mv} \]
This means that as the velocity (\( v \)) of the electron increases, the wavelength (\( \lambda \)) decreases.

### Step 3: Evaluate the options
Now, let’s evaluate the provided options based on the relationship we established:
- **Option A**: Wavelength increases with the increase in the speed of the electron. **(Incorrect)**
- **Option B**: Wavelength remains the same. **(Incorrect)**
- **Option C**: Wavelength decreases with the increase in the speed of the electron. **(Correct)**
- **Option D**: Wavelength changes with the atomic number. **(Incorrect)**

### Conclusion
The correct answer is **Option C**: Wavelength decreases with the increase in the speed of the electron.

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