The position of a neutron in nucleus is known within an uncertainty of #5 xx 10^(-15) "m"#. At what speeds might we expect to find it moving?

Question

1377 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-02-12T20:55:57

#Deltav = 6.30 xx 10^6 "m/s"#

Well, if the uncertainty in the position is known, we wouldn't know the actual speed, only the uncertainty.

#DeltaxDeltap_x >= ℏ//2#

is the Heisenberg Uncertainty Principle. We know that #p = mv# is the linear momentum, so its uncertainty is

#Deltap = mDeltav#

That means

#DeltaxmDeltav >= ℏ//2#

Or

#Deltav >= (ℏ//2)/(mDeltax)#

That means the minimum uncertainty in speed is:

#Deltav_"min" = ((6.626 xx 10^(-34) "J"cdot"s")/(4pi))/(1.675 xx 10^(-27) "kg" cdot 5 xx 10^(-15) "m")#

#= 6.30 xx 10^(6) "m/s"#

Or,

#color(blue)(Deltav >= 6.30 xx 10^(6) "m/s")#

But we know nothing about the actual value of #v#. All we can say is that the speed is:

#"speed" = (v pm 6.30 xx 10^6) "m/s"#

The position of a neutron in nucleus is known within an uncertainty of #5 xx 10^(-15) "m"#. At what speeds might we expect to find it moving?