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Chapter 6: Q45E (page 1315)

(a) The uncertainty in the y-component of a proton鈥檚 position is2.0脳10-12m. What is the minimum uncertainty in a simultaneous measurement of the y-component of the proton鈥檚 velocity? (b) The uncertainty in the z-component of an electron鈥檚 velocity is 0.250 m/s. What is the minimum uncertainty in a simultaneous measurement of the z-coordinate of the electron?

Short Answer

Expert verified
  1. The minimum uncertainty in the proton's y-component speed is1.58脳104m/s
  2. The minimum uncertainty in the proton鈥檚 z-component position is2.32脳10-4m

Step by step solution

01

Heisenberg’s uncertainty principle

According to Heisenberg's uncertainty principle, it is impossible to precisely measure or calculate an object's position and momentum.

鈭�y鈭�py鈮�h/2

02

The minimum uncertainty in a simultaneous measurement of the y-component of the proton’s velocity

a. Using the Heisenberg鈥檚 certainty principle

As;

So, the equation is;

Putting the values,

Hence, the minimum uncertainty in the proton's y-component speed is

03

The minimum uncertainty in a simultaneous measurement of the z-coordinate of the electron

b. Solving for 鈭�z

Putting the values,

Hence, the minimum uncertainty in the proton鈥檚 z-component position is

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