**Questions 1-70 in this thread are questions that imitate those of the real PGRE test. For those of you who want to practise only on ETS official questions there are directions on how to do this (the 5 practice tests etc.).**

**The questions I post here periodically are for those who want to practise on PGRE questions beyond the official material. The questions in this thread are updated when possible!**

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Notice:ALL ANSWERS TO THE FOLLOWING SAMPLE QUESTIONS ARE GIVEN BELOW IN THIS THREAD (TBA answers will be given soon!)

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Notice:

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**Time alloted: Use as much as you need for practice!**

**SAMPLE QUESTION 1**:

Suppose $$\psi_1$$ and $$\psi_2$$ are the ground state wavefunctions of two single (non-interacting) potential wells #1 and #2 respectively. Consider the following wavefunctions representing the ground state of the system of the two aforementioned wells (now seen as a double well):

I. $$\frac{1}{\sqrt{2}}(\psi_1+\psi_2)$$

II. $$\frac{1}{2}(\psi_1 + \sqrt{3} \psi_2)$$

III. $$\frac{1}{\sqrt{2}}(\psi_1-\psi_2)$$

Given the above information which of the following statements is FALSE?

(A) Wavefunction (I) can represent the ground state of a system of two identical wells.

(B) Wavefunction (II) can represent the ground state of an asymmetric double well.

(C) Wavefunction (III) cannot represent the ground state of a symmetric double well.

(D) If the double well is described by wavefunction (II), then potential well #2 is deeper than potential well #1.

(E) If the double well is described by wavefunction (I) its fundamental energy level lies higher than the fundamental energy levels of the non-interacting wells.

**SAMPLE QUESTION 2**:

A beam of radioactive particles is measured as it shoots through a laboratory. It is found that, on average, each particle "lives" for a time of 20 ns. When at rest in the laboratory, the same particles "live" 7 ns on average. How fast do the particles in the beam move?

(A) 0.50c

(B) 0.88c

(C) 0.12c

(D) 0.65c

(E) 0.93c

{c = speed of light}

**SAMPLE QUESTION 3**:

A diffraction grating with a width of 2.0 cm contains 1000 lines/cm across that width. For an incident wavelength of 500 nm, what is the smallest wavelength difference this grating can resolve in the second order?

(A) 0.125 nm

(B) 0.25 nm

(C) 0.50 nm

(D) 8 nm

(E) 2 nm

**SAMPLE QUESTION 4**:

If the temperature $$T$$ of an ideal gas is increased at constant pressure, what happens to the mean free path of its molecules/atoms?

(A) It decreases in proportion to $$1/T$$.

(B) It decreases in proportion to $$1/T^2$$.

(C) It increases in proportion to $$T$$.

(D) It increases in proportion to $$T^2$$.

(E) It is not affected by the temperature change.