The de-Broglie waves associated with an electron moving under a potential difference of 100 V will have wavelength :

Options

A. `12.27 xx 10^(-11)`
B. `12.27 xx 10^(-10)`m
C. `12.27 xx 10^(-9)` m
D. 1 m

Answer

To find the de-Broglie wavelength associated with an electron moving under a potential difference of 100 V, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula**: The de-Broglie wavelength (\( \lambda \)) of an electron accelerated through a potential difference (\( V \)) is given by the formula:
\[ \lambda = \frac{12.27}{\sqrt{V}} \text{ (in Ångströms)} \]
where \( V \) is the potential difference in volts.

2. **Substitute the Given Value**: Here, the potential difference \( V \) is given as 100 V. We will substitute this value into the formula:
\[ \lambda = \frac{12.27}{\sqrt{100}} \]

3. **Calculate the Square Root**: Calculate the square root of 100:
\[ \sqrt{100} = 10 \]

4. **Perform the Division**: Now, substitute the square root back into the equation:
\[ \lambda = \frac{12.27}{10} = 1.227 \text{ Å} \]

5. **Convert Ångströms to Meters**: To convert the wavelength from Ångströms to meters, we use the conversion factor \( 1 \text{ Å} = 10^{-10} \text{ m} \):
\[ \lambda = 1.227 \times 10^{-10} \text{ m} = 1.227 \times 10^{-11} \text{ m} \]

6. **Final Result**: The wavelength of the de-Broglie waves associated with the electron is:
\[ \lambda \approx 1.227 \times 10^{-11} \text{ m} \]

### Conclusion:
The correct answer is option A: \( 1.227 \times 10^{-11} \text{ m} \).