Sample 1Medium
What is the de Broglie wavelength of an electron moving with a velocity of 2.2 × 10^6 m s^-1? (Mass of electron = 9.1 × 10^-31 kg, h = 6.626 × 10^-34 J s)
- A
3.31 × 10^-12 m
- B
3.31 × 10^-8 m
- C
1.51 × 10^-10 m
- D
3.31 × 10^-10 m
Show the answer
The answer is D.λ = h/mv = 6.626 × 10^-34 / (9.1 × 10^-31 × 2.2 × 10^6) = 6.626 × 10^-34 / 2.002 × 10^-24 = 3.31 × 10^-10 m (331 pm).
- A.
The power of ten is wrong by a factor of 100; the product mv is 2.0 × 10^-24 kg m s^-1.
- B.
The power of ten is wrong by a factor of 100 in the other direction.
- C.
This value does not follow from h/mv with the given data; it would require a momentum about twice as large.
NCERT: Class 11 Chemistry, Chapter 2, 2.5
Sample 2NEET level
Consider the following statements: I. The wavelength associated with a moving particle of mass m and velocity v is λ = h/mv. II. The uncertainties in position and momentum of an electron obey Δx × Δp ≥ h/4π. III. The uncertainty principle has significant effects on the motion of macroscopic objects. IV. The wave nature of the electron was confirmed experimentally by the diffraction of an electron beam. Which of the statements are correct?
- A
I and III only
- B
II and III only
- C
I, II and III only
- D
I, II and IV only
Show the answer
The answer is D.de Broglie's relation λ = h/mv and Heisenberg's Δx × Δp ≥ h/4π are both correct, and de Broglie's prediction was confirmed when electron beams were found to undergo diffraction. The uncertainty principle is significant only for microscopic objects; for macroscopic objects the uncertainties are negligible, so III is false.
- A.
Statement III is false, and II and IV are also correct.
- B.
Statement III is false, and I and IV are also correct.
- C.
Statement III is false, and IV is correct.
NCERT: Class 11 Chemistry, Unit 2 (Structure of Atom), Towards Quantum Mechanical Model of the Atom: Dual Behaviour of Matter and Heisenberg's Uncertainty Principle