Question

Calculate 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. \(2.27\,\text{\AA}\)

Hint:

For electrons accelerated through a potential \(V\), remember the shortcut formula: \[ \lambda(\text{\AA}) = \frac{12.27}{\sqrt{V}} \] This avoids lengthy substitutions of physical constants.

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 potential difference. \[ V = 100\,\text{V} \] \[ \lambda = \frac{12.27}{\sqrt{100}} \]

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