A ping pong ball of mass m = 4.9 gram is precisely measured in position to an accuracy of 10^-10 m. What must be the uncertainty in its velocity (in 10^-20 m/s)?
(delta_x)(delta_p) > h/4pi
(delta_x)(m)(delta_v) > h/4pi
(10*10^-10)(0.0049kg)(delta_v) > (6.63*10^-34)/4pi
delta_v = 1.076731911*10^-23 m/s
= 1.08*10^-23 m/s
Is that correct? And how do I put that in terms of 10^-20 m/s?
I tried:
1.08/x = (10^-23)/(10^-20)
x = 1076.731911 m/s = 1080 m/s
But apparently that is incorrect...
1.08*10^-23 m/s
= .108 * 10^22
= .0108 * 10^-21
=.00108 * 10^20 :)
divide the left by ten if you multiply the right by 10
(delta_x)(delta_p) > h/4pi
(delta_x)(m)(delta_v) > h/(4pi*0.0049kg)
(10*10^-10)(0.0049kg)(delta_v)> (6.63*10^-34)/4pi*0.0049kg)
deltaV>(6.63*10^-24)/4pi>1.08E-22 so in terms of E-20,
deltaV>.00108
so in terms of E-20, deltaV>5.2#
Your initial steps in solving the equation are correct, but the mistake occurred when converting the result from meters per second (m/s) to 10^-20 m/s.
To convert the result to 10^-20 m/s, you can do the following:
1. Take the result in m/s (1.08 * 10^-23 m/s) and divide it by 10^-20.
(1.08 * 10^-23 m/s) / (10^-20) = 1.08 * 10^-3
So, the correct uncertainty in velocity, expressed in 10^-20 m/s, is 1.08 * 10^-3.