# What is the velocity of the electron in He+?

### 1 Answer

Relevance

- NCSLv 74 weeks ago
For the nth orbital, the energy is

E(n)=Z² * q⁴ * m / 8ε₀²n²h²

and

E = ½mv²

so

½mv² = Z² * q⁴ * m / 8ε₀²n²h²

means that

v² = 2 * Z² * q⁴ * m / 8ε₀²n²h²

v = Z*q² / 2ε₀nh

Z = atomic # = 2

q = electron charge

ε₀ = 8.85e-12 C²/N·m²

n = state number (assumed 1, lowest energy orbital)

h = Planck's constant = 6.626e-34kg·m²/s

so

v = 2*(1.6e-19C)² / 2*8.85e-12C²/N·m²*1*6.626e-34kg·m²/s

v = 4.4e6 m/s

just over 1% of c

- Log in to reply to the answers

Still have questions? Get answers by asking now.