Given below are two statements: Statement (I): It is impossible to specify simultaneously with arbitrary precision, 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:
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.
Official Solution
Correct Option:
(2)
- Statement I: This is a restatement of the Heisenberg Uncertainty Principle, which asserts that it is impossible to precisely determine both the position and the momentum of a particle simultaneously. This statement is true. - Statement II: The Heisenberg Uncertainty Principle provides the relationship between the uncertainty in position ( ) and momentum ( ), given by: For an electron, if the uncertainties in position and momentum are equal, the uncertainty in velocity can be expressed as: This statement is also correct. Therefore, the correct answer is Both Statement I and Statement II are true.
02
PYQ 2026
medium
chemistryID: jee-main
Two positively charged particles are accelerated by . The masses of particles are and .If the de-Broglie wavelength is times of the second particle , determine the value of .
Official Solution
Correct Option:
(1)
Concept:
The de-Broglie wavelength of a particle accelerated through a potential difference is given by:
For particles accelerated through the same potential difference , wavelength depends only on the square root of mass :
Step 1: Write Ratio of Wavelengths
Step 2: Substitute Given Values
Step 3: Determine
About Quantum Mechanics - JEE-MAIN
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