Question 1

The graph below represents a wave function $\Psi$(x) for a particle confined to -2.00 m $\le$ x $\le$ +2.00 m.The value of the normalisation constant A may be:

Accepted Answer

A)   
B)   
C)   
D)   
E)  either or    C

Question 2

A particle has a total energy that is less than that of a potential barrier.When the particle penetrates the barrier, its wave function is:

Accepted Answer

A)  a positive constant.
B)  exponentially increasing.
C)  oscillatory.
D)  exponentially decreasing.
E)  none of the above. D

Question 3

When U(x) is infinitely large elsewhere, the wave function of a particle restricted to the region 0 < x < L where U(x) = 0, may have the form $\Psi$(x) =

Accepted Answer

A)   
B)   
C)  Aen  π\piπ x / L.
D)   
E)     A

Question 4

A physically reasonable wave function, $\Psi$(x), for a one-dimensional system must:

Accepted Answer

A)  be defined at all points in space.
B)  be continuous at all points in space.
C)  be single-valued.
D)  obey all the constraints listed above.
E)  obey only (b)  and (c)  above.

Question 5

What is the quantum number n of a particle of mass m confined to a one-dimensional box of length L when its momentum is 4h/L?

Accepted Answer

A)  1
B)  4
C)  2
D)  8
E)  16

Question 6

The wave function $\Psi$(x) of a particle confined to 0 $\le$ x $\le$ L is given by $\Psi$(x) = Ax.$\Psi$(x) = 0 for x  L.When the wave function is normalised, the probability density at coordinate x has the value:

Accepted Answer

A)    L.When the wave function is normalised, the probability density at coordinate x has the value: 
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Question 7

The expectations value of a function f(x) of x when the wave function depends only on x is given by  =

Accepted Answer

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Question 8

Assume we can determine the position of a particle within an uncertainty of 0.5 nm.What will be the resulting uncertainty in the particle's momentum (in kg . m/s)?

Accepted Answer

A)  1.9 *10-25
B)  4.2 *10-25
C)  1.1 * 10-25
D)  1.3 *10-24
E)  6.6 *10-25

Question 9

Find the uncertainty in the momentum (in kg .m/s) of an electron if the uncertainty in its position is equal to 3.4 * 10-10 m, the circumference of the first Bohr orbit.

Accepted Answer

A)  6.2 * 10-25
B)  1.6 * 10-25
C)  15.5 * 10-25
D)  19.4 * 10-25
E)  2.0 * 10-24

Question 10

Find the kinetic energy (in terms of Planck's constant) of a football (m = 1 kg) confined to a one-dimensional box that is 25 cm wide if the baseball can be treated as a wave in the ground state.

Accepted Answer

A)  3 h2
B)  2 h2
C)  h2
D)  4h2
E)  0.5 h2

Question 11

The wave function for a particle in a one-dimensional box is .Which statement is correct?

Accepted Answer

A)  This wave function gives the probability of finding the particle at x.
B)  | Ψ\PsiΨ (x) |2 gives the probability of finding the particle at x.
C)  | Ψ\PsiΨ (x) |2  Δ\DeltaΔ x gives the probability of finding the particle between x and x +  Δ\DeltaΔ x.
D)  gives the probability of finding the particle at a particular value of x. 
E)  gives the probability of finding the particle between x and x +  Δ\DeltaΔ x.

Question 12

If the position of an electron (m = 9.11 *10-31 kg) could be measured to within 10S1U1P1-30S1S1P0 m, the uncertainty in the magnitude of its speed could be as much as

Accepted Answer

A)  6 *10-34 m/s.
B)  6 *1025 m/s.
C)  6 * 1030 m/s.
D)  1031 m/s.
E)  1061 m/s.

Question 13

A particle in a finite potential well has energy E, as shown below.  The wave function in region III where x > L has the form $\Psi$III =

Accepted Answer

A)  Ae-Cx.
B)  AeCx.
C)  F sin kx.
D)  G cos kx.
E)  F sin kx + G cos kx.

Question 14

A particle is in the second excited state of a one-dimensional box of length 1.0 m.What is its momentum (in kg . m/s)?

Accepted Answer

A)  6.6 *10-34
B)  3.3 * 10-34
C)  9.9 *10-34
D)  13 * 10-34
E)  cannot be solved unless mass of particle is known

Question 15

An electron is sitting on a pinpoint having a diameter of 2.5 $\mu$m.What is the minimum uncertainty in the speed of the electron?

Accepted Answer

The answer of An electron is sitting on a pinpoint...

Question 16

The graph below shows the value of the probability density $\Psi$(x)|2 in the region-3.00 m $\le$ x $\le$+3.00 m.The value of the constant A is:

Accepted Answer

A)   
B)   
C)   
D)   
E)  either or

Question 17

If the interaction of a particle with its environment restricts the particle to a finite region of space, the result is the quantisation of ____ of the particle.

Accepted Answer

A)  the momentum
B)  the energy
C)  the velocity
D)  all of the above properties
E)  only properties (a)  and (b)

Question 18

Because the factor h on the right side of the Heisenberg uncertainty principle has units of Joule-seconds, it suggests that the energy of a system also has uncertainty.The uncertainty in energy depends on the length of the time interval during which a system exists.$\Delta$E$\Delta$t $\ge$h/4 $\pi$.Suppose an unstable mass is produced during a high-energy collision such that the uncertainty in its mass is me/100.(me = 9.11*10-31 kg.) How long will this particle exist?

Accepted Answer

A)  6.4 * 10-20 s
B)  2.3 * 10-23 s
C)  1.0 * 1015 s
D)  1.2 *1013 s
E)  8.1 * 10-19 s

Question 19

A particle is in the ground state of a one-dimensional box of length 1.0 m.What is the minimum value of its momentum (in kg .m/s)?

Accepted Answer

A)  9.9 * 10-34
B)  6.6 * 10-34
C)  3.3 * 10-34
D)  13 * 10-34
E)  cannot be solved unless mass of particle is known.

Question 20

Suppose we use optical radiation ($\lambda$= 500 nm) to determine the position of the electron to within the wavelength of the light.What will be the resulting uncertainty in the electron's velocity?

Accepted Answer

The answer of Suppose we use optical radiation ($\lambda$= 500...

Exam 18: Introduction to Quantum Mechanics

A particle has a total energy that is less than that of a potential barrier.When the particle penetrates the barrier, its wave function is:

When U(x) is infinitely large elsewhere, the wave function of a particle restricted to the region 0 < x < L where U(x) = 0, may have the form $\Psi$ (x) =

A physically reasonable wave function, $\Psi$ (x) , for a one-dimensional system must:

What is the quantum number n of a particle of mass m confined to a one-dimensional box of length L when its momentum is 4h/L?

The wave function $\Psi$ (x) of a particle confined to 0 $\le$ x $\le$ L is given by $\Psi$ (x) = Ax. $\Psi$ (x) = 0 for x < 0 and x > L.When the wave function is normalised, the probability density at coordinate x has the value:

The expectations value of a function f(x) of x when the wave function depends only on x is given by < f(x) > =

Assume we can determine the position of a particle within an uncertainty of 0.5 nm.What will be the resulting uncertainty in the particle's momentum (in kg . m/s) ?

Find the uncertainty in the momentum (in kg .m/s) of an electron if the uncertainty in its position is equal to 3.4 * 10-10 m, the circumference of the first Bohr orbit.

Find the kinetic energy (in terms of Planck's constant) of a football (m = 1 kg) confined to a one-dimensional box that is 25 cm wide if the baseball can be treated as a wave in the ground state.

If the position of an electron (m = 9.11 *10-31 kg) could be measured to within 10^-30 m, the uncertainty in the magnitude of its speed could be as much as

A particle is in the second excited state of a one-dimensional box of length 1.0 m.What is its momentum (in kg . m/s) ?

An electron is sitting on a pinpoint having a diameter of 2.5 $\mu$ m.What is the minimum uncertainty in the speed of the electron?

If the interaction of a particle with its environment restricts the particle to a finite region of space, the result is the quantisation of ____ of the particle.

A particle is in the ground state of a one-dimensional box of length 1.0 m.What is the minimum value of its momentum (in kg .m/s) ?

Suppose we use optical radiation ( $\lambda$ = 500 nm) to determine the position of the electron to within the wavelength of the light.What will be the resulting uncertainty in the electron's velocity?

Exam 18: Introduction to Quantum Mechanics

The graph below represents a wave function Ψ\PsiΨ (x) for a particle confined to -2.00 m ≤\le≤ x ≤\le≤ +2.00 m.The value of the normalisation constant A may be:

A particle has a total energy that is less than that of a potential barrier.When the particle penetrates the barrier, its wave function is:

When U(x) is infinitely large elsewhere, the wave function of a particle restricted to the region 0 < x < L where U(x) = 0, may have the form Ψ\PsiΨ (x) =

A physically reasonable wave function, Ψ\PsiΨ (x) , for a one-dimensional system must:

What is the quantum number n of a particle of mass m confined to a one-dimensional box of length L when its momentum is 4h/L?

The wave function Ψ\PsiΨ (x) of a particle confined to 0 ≤\le≤ x ≤\le≤ L is given by Ψ\PsiΨ (x) = Ax. Ψ\PsiΨ (x) = 0 for x < 0 and x > L.When the wave function is normalised, the probability density at coordinate x has the value:

The expectations value of a function f(x) of x when the wave function depends only on x is given by < f(x) > =

Assume we can determine the position of a particle within an uncertainty of 0.5 nm.What will be the resulting uncertainty in the particle's momentum (in kg . m/s) ?

Find the uncertainty in the momentum (in kg .m/s) of an electron if the uncertainty in its position is equal to 3.4 * 10-10 m, the circumference of the first Bohr orbit.

Find the kinetic energy (in terms of Planck's constant) of a football (m = 1 kg) confined to a one-dimensional box that is 25 cm wide if the baseball can be treated as a wave in the ground state.

The wave function for a particle in a one-dimensional box is .Which statement is correct?

If the position of an electron (m = 9.11 *10-31 kg) could be measured to within 10-30 m, the uncertainty in the magnitude of its speed could be as much as

A particle in a finite potential well has energy E, as shown below. The wave function in region III where x > L has the form Ψ\PsiΨ III =

A particle is in the second excited state of a one-dimensional box of length 1.0 m.What is its momentum (in kg . m/s) ?

An electron is sitting on a pinpoint having a diameter of 2.5 μ\muμ m.What is the minimum uncertainty in the speed of the electron?

The graph below shows the value of the probability density Ψ\PsiΨ (x) |2 in the region-3.00 m ≤\le≤ x ≤\le≤ +3.00 m.The value of the constant A is:

If the interaction of a particle with its environment restricts the particle to a finite region of space, the result is the quantisation of ____ of the particle.

A particle is in the ground state of a one-dimensional box of length 1.0 m.What is the minimum value of its momentum (in kg .m/s) ?

Suppose we use optical radiation ( λ\lambdaλ = 500 nm) to determine the position of the electron to within the wavelength of the light.What will be the resulting uncertainty in the electron's velocity?

When U(x) is infinitely large elsewhere, the wave function of a particle restricted to the region 0 < x < L where U(x) = 0, may have the form $\Psi$ (x) =

A physically reasonable wave function, $\Psi$ (x) , for a one-dimensional system must:

The wave function $\Psi$ (x) of a particle confined to 0 $\le$ x $\le$ L is given by $\Psi$ (x) = Ax. $\Psi$ (x) = 0 for x < 0 and x > L.When the wave function is normalised, the probability density at coordinate x has the value:

If the position of an electron (m = 9.11 *10-31 kg) could be measured to within 10^-30 m, the uncertainty in the magnitude of its speed could be as much as

An electron is sitting on a pinpoint having a diameter of 2.5 $\mu$ m.What is the minimum uncertainty in the speed of the electron?

Suppose we use optical radiation ( $\lambda$ = 500 nm) to determine the position of the electron to within the wavelength of the light.What will be the resulting uncertainty in the electron's velocity?