Question

A 4.6 × 〖10〗^(-2) kg golf ball is in motion along the x-axis. if it is located at the position x = 1.00m, with an uncertainty of 0.005m, find the uncertainty in the determination of momentum and velocity of the golf- ball.

Answer 1

It has given that,

mass of golf ball, m = 4.6 × 10¯² kg

position of ball, x = 1 m

uncertainty in the position, ∆x = 0.005 m

To find : uncertainty in the determination of momentum and velocity of the golf ball.

solution : from Heisenberg's uncertainty principle,

∆P × ∆x = h/4π

⇒∆p × 0.005 m = (6.63 × 10¯³⁴ Js)/(4 × 3.14)

⇒∆p = (6.63 × 10¯³⁴)/(4 × 3.14 × 0.005)

= 105.57 × 10¯³⁴ Kg m/s

= 1.0557 × 10¯³² kg m/s

Therefore the uncertainty in the momentum is 1.0557 × 10¯³² kg m/s.

uncertainty in the velocity of the golf ball, ∆v = ∆P/m

= (1.0557 × 10¯³²)/(4.6 × 10¯²)

= 0.2295 × 10¯³⁰

= 2.295 × 10¯³¹ m/s