8 27.1 The Heisenberg uncertainty principles c. The fraction of the speed of light 4.0×10 =0.13 c3.0×10 y ≈1.0 It is reasonable to express its momentum in classical expression. s 27.1 The Heisenberg uncertainty principles >Implications of the energy-time uncertainty principle a. The mass of fundamental particles According to special relativity Em=mc2→AEt=c2m According to the energy-time uncertainty principle c2AmAt≥h The mean lifetime of a free neutron is 888 s then 6.626×10 =829×10-k c2r(3×105)2(88》7 c. The fraction of the speed of light 1.0 1 / 1 0.13 3.0 10 4.0 10 2 2 8 7 ≈ − = = × × = v c c v γ It is reasonable to express its momentum in classical expression. §27.1 The Heisenberg uncertainty principles ¾Implications of the energy-time uncertainty principle a. The mass of fundamental particles According to special relativity E mc ∆E c ∆m 2 rest 2 rest = ⇒ = According to the energy-time uncertainty principle c ∆m∆t ≥ h 2 8.29 10 kg (3 10 ) (888) 6.626 10 54 8 2 34 2 − − = × × × = = c t h m ∆ ∆ The mean lifetime of a free neutron is 888 s, then §27.1 The Heisenberg uncertainty principles