Statement (I) : It is impossible to specify simultaneously with arbitrary precision, both the linear momentum and the position of a particle.

Question

Given below are two statements :

Statement (I) : It is impossible to specify simultaneously with arbitrary precision, both the linear momentum and the position of a particle.

Statement (II) : If the uncertainty in the measurement of position and uncertainty in measurement of momentum are equal for an electron, then the uncertainty in the measurement of velocity is \(\geq \sqrt{\frac{h}{\pi}} \times \frac{1}{2 \mathrm{m}}.\)

In the light of the above statements, choose the correct answer from the options given below :

(1) Statement I is true but Statement II is false.

(2) Both Statement I and Statement II are true.

(3) Statement I is false but Statement II is true.

(4) Both Statement I and Statement II are false.

Answer 1

Correct option is (2) Both Statement I and Statement II are true.

According to Heisenberg’s uncertainty principle, it is impossible to determine simultaneously the exact position and momentum of particle like electron 

If \(\Delta p=\Delta x \)

\( \Delta p . \Delta x \geq \frac{h}{4 \pi} \)

\((\Delta p)^2 \geq \frac{h}{4 \pi} \)

\(\Delta p \geq \sqrt{\frac{h}{\pi}} \times \frac{1}{2} \)

\(m \Delta v \geq \sqrt{\frac{h}{\pi}} \times \frac{1}{2} \)

\(\Delta v \geq \sqrt{\frac{h}{\pi}} \times \frac{1}{2 m}\)