Question

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

• A. \(1.227\,\text{\AA}\)
• B. \(0.612\,\text{\AA}\)
• C. \(2.45\,\text{\AA}\)
• D. \(3.12\,\text{\AA}\)

Hint:

For electrons accelerated through potential \(V\): \[ \lambda=\frac{12.27}{\sqrt{V}} \text{ \AA} \] This shortcut formula is commonly used in quantum mechanics problems.

Answer 1

The Correct Option is A

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

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

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