Question

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

• A. \(1.227\,\text{\AA}\)
• B. \(12.27\,\text{\AA}\)
• C. \(0.1227\,\text{\AA}\)
• D. \(122.7\,\text{\AA}\)

Hint:

For electrons accelerated through a potential \(V\), remember the shortcut formula \(\lambda = \frac{12.27}{\sqrt{V}}\,\text{\AA}\). It is widely used in quick numerical problems related to matter waves.

Answer 1

The Correct Option is A

Concept: According to de Broglie's hypothesis, a moving particle exhibits wave nature. For an electron accelerated through a potential difference \(V\), the wavelength is given by the shortcut formula: \[ \lambda = \frac{12.27}{\sqrt{V}} \, \text{\AA} \] where \(V\) is the accelerating potential in volts.

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

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