Question

Calculate the de-Broglie wavelength of an electron accelerated through a potential difference of \(100\text{ V}\).

• A. \(1.227\ \text{Å}\)
• B. \(0.1227\ \text{nm}\)
• C. \(12.27\ \text{nm}\)
• D. \(0.01227\ \text{nm}\)

Hint:

For electrons accelerated through potential \(V\), quickly use \( \lambda = \dfrac{12.27}{\sqrt{V}} \) Å. This shortcut is widely used in electron diffraction and microscopy problems.

Answer 1

The Correct Option is A

Concept: The de-Broglie wavelength of an electron accelerated through a potential difference \(V\) is given by \[ \lambda = \frac{h}{p} \] For an electron accelerated through potential \(V\), the simplified formula is \[ \lambda = \frac{12.27}{\sqrt{V}} \ \text{Å} \] where \(V\) is in volts.
Step 1: {Substitute the given potential difference.} \[ V = 100 \ \text{V} \] \[ \lambda = \frac{12.27}{\sqrt{100}} \]
Step 2: {Evaluate the expression.} \[ \sqrt{100} = 10 \] \[ \lambda = \frac{12.27}{10} \] \[ \lambda = 1.227 \ \text{Å} \]