source : science20.com
“It is impossible to measure simultaneously the position and momentum or velocity of a small moving particle with absolute accuracy”.
Heisenberg principle is represented in equation form as follows-
(ΔP)( Δx) >= h/4π
mΔV.Δx >= h/4π
ΔV.Δx >= h/4πm
Product of uncertainty in position &momentum is greater or equal to h/4π
Solved Numerical Problems
Question 1. The mass of an electron is 9.1×10–31 kg. Its uncertainty in velocity is 5.7×105 m/sec. Calculate uncertainty in its position?
Ans. m= 9×10–31
ΔV= 5.7×105 m/sec Δx=?
h= 6.6×10–34 Joule-Sec.
Question 2.The mass of a ball is 0.15 kg & its uncertainty in position to 10–10m. What is the value of uncertainity in its velocity?
Ans. m=0.15 kg. h=6.6×10-34 Joule-Sec.
Δx = 10 –10 m
Question 3.The mass of a bullet is 10gm & uncertainity in its velocity is 5.25×10–26 cm/sec. Calculate the uncertainity in its position?
Ans. m=10 gm. h=6.6×10–27 erg-sec
Δv= 5.25×10–26 cm
≥ 1×10–3 cm
Question 4.The uncertainity for the calculation of radius of the 1st Bohr Orbit is 2% for the H-atom. What will be the uncertainity in velocity of electron in the 1st Bohr Orbit (h=6.626×10–34Joule-Sec, m=9.1×10–31kg)
Ans. r= (0.529 n*n/2 )A0
for Bohr’s 1st orbit
r = 0.529 A
= 0.529×10–10 m