Question

Determine the de Broglie wavelength of an electron accelerated through \(100\,V\).

• 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 the shortcut \[ \lambda = \frac{12.27}{\sqrt{V}} \; \text{\AA}. \] This formula is widely used in quantum mechanics and electron diffraction problems.

Answer 1

The Correct Option is B

Concept: According to the de Broglie hypothesis, a moving particle exhibits wave-like properties. The wavelength associated with a charged particle accelerated through a potential difference \(V\) is given by \[ \lambda = \frac{h}{p} \] For electrons accelerated through a potential \(V\), this simplifies to \[ \lambda = \frac{12.27}{\sqrt{V}} \; \text{\AA} \] where \(V\) is in volts.

Step 1: Write the de Broglie wavelength formula for an electron. \[ \lambda = \frac{12.27}{\sqrt{V}} \; \text{\AA} \]

Step 2: Substitute the given potential difference. \[ V = 100 \] \[ \lambda = \frac{12.27}{\sqrt{100}} \]

Step 3: Evaluate the expression. \[ \lambda = \frac{12.27}{10} \] \[ \lambda = 1.227 \; \text{\AA} \]