Question

What is the de Broglie wavelength of an electron accelerated through a potential difference of \(100\,\text{V}\)?

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

Hint:

For electrons accelerated through a potential \(V\), quickly use \[ \lambda(\text{\AA}) = \frac{12.27}{\sqrt{V}} \] This shortcut is widely used in quantum mechanics problems.

Answer 1

The Correct Option is B

Concept: The de Broglie wavelength of an electron accelerated through a potential difference \(V\) is given by \[ \lambda = \frac{12.27}{\sqrt{V}} \ \text{\AA} \] where \(V\) is in volts.

Step 1: Substitute the given potential difference. \[ V = 100 \] \[ \lambda = \frac{12.27}{\sqrt{100}} \]

Step 2: Simplify the expression. \[ \sqrt{100} = 10 \] \[ \lambda = \frac{12.27}{10} \] \[ \lambda = 1.227 \ \text{\AA} \] \[ \boxed{\lambda = 1.227 \ \text{\AA}} \]