Question

Electron 1 is accelerated from rest through a potential difference of 100 V. Electron 2 is accelerated from rest through a potential difference of 200 V. Afterward, which electron has the larger de Broglie wavelength? Explain

Short answer

Electron 1 will have a higher de-broglie wavelength.

Step-by-step solution

Step 1. Given information is :Electron 1 and electron 2 are accelerated starting from rest through a potential difference of 100 V and 200 V respectively.

We need to find out that which of the electron will have a higher De-Broglie wavelength.

Step 2. Comparing as per the formula of De-Broglie Wavelength.

$$\begin{gathered} K_1=100V \\ {K}_2=200V \\ {K}_1<K_2 \\ De-BroglieWavelength,\lambda =\frac{h}{\sqrt{2mK}} \\ Itmeans\lambda isinverselyproportionaltoK. \\ So,As{K}_1<K_2 \\ \Rightarrow {\lambda }_1>{\lambda }_2 \end{gathered}$$

Electron 1 will have a higher de-broglie wavelength.