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 .
In the light of the above statements, choose the correct answer from the options given below :
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 .
In the light of the above statements, choose the correct answer from the options given below :
- (A)Statement I is true but Statement II is false.
- (B)Both Statement I and Statement II are true.✓ Correct
- (C)Statement I is false but Statement II is true.
- (D)Both Statement I and Statement II are false.
Answer: (B)
Solution
The uncertainty principle, , forbids simultaneous exact knowledge of a particle's position and momentum — statement I is correct. Setting , the inequality becomes , so . Since , dividing through by mass gives exactly the bound stated in statement II. Both statements are correct.
JEE Main · 2025 · 29 Jan 2025 · Shift 2 · Single correct option