Answer to Question #314243 in Molecular Physics | Thermodynamics for BIGIRIMANA Elie

Question

A hydrogen atom is 5.3 × 10−10 m in radius. Use the uncertainty principle to estimate the minimum energy an electron can have in this atom. 

Answer 1

Answer

According to uncertainty

$P=\frac{\hbar}{r}\\=2.11*10^{-20}kg-m/s$

So minimum energy

$E=\sqrt{p^2c^2+m^2c^4}$

Putting all values

E=$3.3*10^{-12}J$