An electron is accelerated through a potential of 120 V. Find its de Broglie wavelength

Answer

To find the de Broglie wavelength of an electron that has been accelerated through a potential of 120 V, we can use the formula:

\[ \lambda = \frac{1.228}{\sqrt{V}} \]

where:
- \(\lambda\) is the de Broglie wavelength in nanometers,
- \(V\) is the accelerating potential in volts.

### Step-by-step Solution:

1. **Identify the given values**:
- The potential \(V = 120 \, \text{V}\).

2. **Substitute the value of \(V\) into the formula**:
\[ \lambda = \frac{1.228}{\sqrt{120}} \]

3. **Calculate \(\sqrt{120}\)**:
- \(\sqrt{120} \approx 10.95\) (you can use a calculator for this step).

4. **Now substitute \(\sqrt{120}\) back into the equation**:
\[ \lambda = \frac{1.228}{10.95} \]

5. **Perform the division**:
\[ \lambda \approx 0.1121 \, \text{nm} \]

### Final Answer:
The de Broglie wavelength of the electron is approximately \(0.1121 \, \text{nm}\).