Question

The de Broglie wavelength associated with an electron accelerated through a potential difference of \( \frac{200}{3} \ \text{V} \) is nearly

• A. \( 25 \ \text{\AA} \)
• B. \( 2.5 \ \text{\AA} \)
• C. \( 15 \ \text{\AA} \)
• D. \( 1.5 \ \text{\AA} \)

Hint:

To find the de Broglie wavelength of an electron, use \( \lambda(\text{\AA}) = \frac{12.27}{\sqrt{V}} \) where \( V \) is in volts.

Answer 1

The Correct Option is D

Step 1: Use the de Broglie wavelength formula for an electron \[ \lambda = \frac{12.27}{\sqrt{V}} \ \text{\AA} \] Step 2: Substitute the given potential \[ V = \frac{200}{3} \Rightarrow \lambda = \frac{12.27}{\sqrt{200/3}} = \frac{12.27}{\sqrt{66.67}} \approx \frac{12.27}{8.16} \approx 1.5 \ \text{\AA} \]