5
a.
Momentum of Electron in this case = , where is the mass of electron [in non-relativistic domain - 9.11 x 10^(-31) Kg] and V is the velocity of electron ( 5 x 10^3 m/s )
Momentum of electron = 9.11 x 10^(-31) Kg x 5 x 10^3 m/s = 4.56 x 10^(-27) Kgm/s
Electron speed has an uncertainity of 0.003%
So the uncertainity in momentum of electron = (0.003/100) x 4.56 x 10^(-27) Kgm/s = 1.37 x 10^(-31) Kgm/s
As per Heisenberg's uncertainity principle
h = 6.63 x 10^(-34) Joule-sec
Hence 1.37 x 10^(-31) Kgm/s x = 6.63 x 10^(-34) Joule-sec / 4
= 6.63 x 10^(-34) J-sec/ [ 1.37 x 10^(-31) Kgm/s x 4 x ] = 4.84 x 10^(-3) m/ 4 x = 3.85 x 10^(-4) metrs
= 0.385 mm
b. Heisenberg's uncertainity principle in Energy and time format is
In this case life time = = 26 x 10^(-9) s
= [6.63 x 10^(-34) J-s/ 4]/ [ 26 x 10^(-9) s] = 2.03 x 10^(-27) J
Meson energy = 140 x 10^6 eV = 140 x 10^6 x 1.6 x 10^(-19 ) J
Uncertainity level = = {2.03 x 10^ (-27) J / [ 140 x 10^6 x 1.6 x 10^(-19)] } x 100
= 9.06 x 10^(-15) %
Level of accuracy = 2.03 x 10^(-27) J/
5, a. Electron speed is measured with an accuracy rate of 0.003% having a speed of...
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