Question
The figure shows the wave functions Y (x) of a particle moving along the x-axis. Which of the following statements correctly interprets this graph?
(A) The particle is oscillating in charge from positive to negative.
(B) The lowest probability of finding the particle is at 3.0 nm.
(C) There is an equal probability of finding the particle at 1.5 nm as at 4.5nm.
(D) The length of the particle is 4 nm.
▶️Answer/Explanation
Ans:
C—The amplitude of the wave function (positive or negative) indicates the probability of finding the particle at that location. The probability of finding the particle is the same at locations 1.5 nm and 4.5 nm.
Question
The graph shows the wave function of a particle as a function of x in the region between-25 nm< x < +25 nm. At which of the following positions is the probability of finding the particle greatest?
(A) -24nm
(B) -15 nm and 0.0 nm
(C) -2nm
(D) 2 nm
▶️Answer/Explanation
Ans:
C
The particle is most likely to be found at the highest positive/negative amplitude location of \(\Psi\) as a function of x. The particle will not be found at locations -15 nm and 0.0 nm.
Question
The wave function of a quantum object vs. position is graphed above. Which of the following correctly ranks the probabilities of observing the particle at the listed positions?
(A) P(x = 0.5 m) > P(x = 2.25 m) > P(x = 1. 75 m)
(B) P(x = 0.5 m) > P(x = 1. 75 m) > P(x = 1.25 m)
(C) P(x = 3.0 m) > P(x = 1. 75 m) > P(x = 2.0 m)
(D) P(x = 3.5 m) > P(x = 3.0 m) > P(x = 1.75 m)
▶️Answer/Explanation
Ans:B
The square of the wave function of a quantum object can be interpreted as the likelihood of an observation occurring at the stated position.
Question
An alien space ship attacks a planet by shooting a laser beam at the planet every five seconds. If the ship is approaching the planet at high speed, which of the following is true for an observer situated on the planet?
(A) The laser beams strike the planet at a frequency of 0.2 Hz.
(B) The laser beams strike the planet at a frequency less than 0.2 Hz.
(C) The laser beams strike the planet at a frequency greater than 0.2 Hz.
(D) More information is needed.
▶️Answer/Explanation
Ans: (C)
The laser beams strike the planet at a frequency greater than 0.2 Hz. As the spaceship approaches the planet while emitting laser beams at a frequency of 0.2 Hz, the observer on the planet will observe a frequency shift to a higher frequency consistent with the Doppler Effect.