Question

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

• 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 \(V\), remember the quick formula \[ \lambda = \frac{12.27}{\sqrt{V}} \ \text{\AA} \] This shortcut avoids lengthy calculations using \( \lambda = \frac{h}{p} \).

Answer 1

The Correct Option is B

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

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

Step 2: Evaluate the square root. \[ \sqrt{100} = 10 \] \[ \lambda = \frac{12.27}{10} \] \[ \lambda = 1.227 \ \text{\AA} \] Thus, the de Broglie wavelength is: \[ \boxed{1.227 \ \text{\AA}} \]