## What is the de Broglie wavelength of an electron in the ground state of a hydrogen atom?

Answer:

λ = 332.5 pm

Explanation:

The formula for the de Broglie wavelength λ is

where

h = Planck’s constant

m = the mass of the electron

v = the speed of the electron.

Calculate the speed of the electron

The energy \(E\) of a hydrogen electron in an orbit is

\(E=-\frac{R_{\mathrm{H}}}{n^{2}}\)where

\(R_{\mathrm{H}}=\) the Rydberg energy constant \(\left(2.180 \times 10^{-18} \mathrm{~J}\right)\)