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Magazine Chapter 6: Q48E (page 1316)
(a) The x-coordinate of an electron is measured with an uncertainty of 0.30 mm. What is the x-component of the electron鈥檚 velocity,
if the minimum percent uncertainty in a simultaneous measurement of
is 1.0% ?(b) Repeat part (a) for a proton.
Short Answer
(a) The x-component of the electron鈥檚 velocity is 19.3m/s.
(b) The x-component of the proton鈥檚 velocity is 0.011m/s.
Step by step solution
Heisenberg’s uncertainty principle
According to Heisenberg's uncertainty principle, it is impossible to precisely measure or calculate an object's position and momentum.
The x-component of the electron’s velocity
(a) Using the Heisenberg uncertainty principle
From the uncertainty in the momentum,
So, the equation is;
Here (m) is the mass of the marble and
is the uncertainty on the x-component.
As
is the uncertainty in an electron's x-coordinate,
is the mass of the electron, and
is the minimum percent uncertainty in a simultaneous measurement of speed.
Thus, putting the values;
Hence, the x-component of the electron鈥檚 velocity is 19.3m/s.
The x-component of the proton’s velocity
(b) For proton,
Hence, the x-component of the proton鈥檚 velocity is 0.011m/s.
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