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Chapter 6: Q47E (page 1316)

A scientist has devised a new method of isolating individual particles. He claims that this method enables him to detect simultaneously the position of a particle along an axis with a standard deviation of 0.12 nm and its momentum component along this axis with a standard deviation of.Use the Heisenberg uncertainty principle to evaluate the validity of this claim.

Short Answer

Expert verified

, this claim is invalid.

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.

02

Evaluating the validity of the claim

The uncertainty in detection is represented by the standard deviation. As a result, the uncertainty in the particle's position is, and the uncertainty in its momentum is along the same axis.

As a result, the product of these two quantities is;

Using the Heisenberg鈥檚 uncertainty principle is;

Hence,, this claim is invalid.

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