# Heisenberg Principle (Nucleus)

1. An electron inside a hydrogen atom is confined to within a space of about 0.110 nm. If the electron mass is $9.11 × 10^{-31}$ kg, what is the uncertainty in the electron’s velocity?

2. In the fission reaction $235U + 1n →141Ba + 92Kr + neutrons$, the number of neutrons produced is:

Answers

1. The uncertainty principle states that

$\Delta(x)*\Delta(p) >= h/(2*\pi)$

where $\Delta(x)$ is the uncertainty in the position, $\Delta(p)$ the uncertainty in the linear momentum and $h$ the Planck constant.

$p = mass*speed = m*v$

Hence $\Delta(v) >= h/m/\Delta(x)/2/\pi =$

$= 6.626*10^{-34}/9.11*10^{-31}/0.110*10^{-9}/2/\pi =1.05*10^6 (m/s)$

2. There are 235+1 = 236 nucleons (protons and neutrons) entering the reaction and only 141+92 =233 nucleons found in the reaction products (Ba and Kr) hence the number of neutrons produced is 3:

$(235)U +(1)n = (141)Ba +(92)Kr +3*(1)n$