Deck 28: Quantum Physics

Question 1

The probability of finding a particle with wave function $\psi$ in an interval $\Delta x$ is given by

A) $\left|\psi^{2}\right|(\Delta x)^{2}$ .
B) $\psi \Delta \mathrm{x}$ .
C) $|\psi|(\Delta x)^{2}$ .
D) $\psi$ .
E) $\left|\psi^{2}\right| \Delta \mathrm{x}$ .

Answer 1

$\left|\psi^{2}\right| \Delta \mathrm{x}$ .

Question 2

What is the de Broglie wavelength of an electron with kinetic energy $1.60 \times 10^{-15} \mathrm{~J}$ ?

A) $1.20 \mathrm{fm}$
B) $12.3 \mathrm{pm}$
C) $13.7 \mathrm{pm}$
D) $61.2 \mathrm{~nm}$
E) $612 \mathrm{~nm}$

Answer 2

$12.3 \mathrm{pm}$

Question 3

What is the energy of a photon that has the same wavelength as an electron with kinetic energy $1.60 \times 10^{-15}$ $\mathrm{J}$ ?

A) $6.77 \mathrm{keV}$
B) $5.53 \mathrm{keV}$
C) $55.3 \mathrm{keV}$
D) $10.0 \mathrm{keV}$
E) $101 \mathrm{keV}$

Answer 3

$101 \mathrm{keV}$

Question 4

What is the de Broglie wavelength of a neutron with kinetic energy $44.0 \mathrm{keV}$ ? The mass of a neutron is 939.6 $\mathrm{MeV} / \mathrm{c}^{2}$ .

A) $2.83 \mathrm{pm}$
B) $5.11 \mathrm{pm}$
C) $56.4 \mathrm{pm}$
D) $0.166 \mathrm{pm}$
E) $0.136 \mathrm{pm}$

Question 5

In the Bohr model of the hydrogen atom, how is the circumference $C_{n}$ of the $n^{\text {th }}$ orbit of the electron related to the de Broglie wavelength $\lambda_{\mathrm{n}}$ of the electron?

A) $\lambda_{\mathrm{n}}=\mathrm{C}_{\mathrm{n}} / \mathrm{n}$
B) $\lambda_{\mathrm{n}}=\mathrm{C}_{\mathrm{n}} / 2 \pi$
C) $\lambda_{\mathrm{n}}=\mathrm{nC}_{\mathrm{n}}$
D) $\lambda_{\mathrm{n}}=\mathrm{C}_{\mathrm{n}} / \mathrm{n}^{2}$
E) $\lambda_{\mathrm{n}}=\mathrm{C}_{\mathrm{n}}$

Question 6

What accelerating potential in an electron microscope would give electrons a wavelength $1.00 \times 10^{-10} \mathrm{~m}$ ?

A) $37.5 \mathrm{~V}$
B) $75.0 \mathrm{~V}$
C) $300 \mathrm{~V}$
D) $150 \mathrm{~V}$

Question 7

Using the energy-time version of the uncertainty principle, estimate the uncertainty in the energy of a state with lifetime of $10^{-9} \mathrm{~s}$ .

A) $10^{-2} \mathrm{eV}$
B) $10^{-7} \mathrm{eV}$
C) $10^{-15} \mathrm{eV}$
D) $10^{-12} \mathrm{eV}$
E) $10^{-18} \mathrm{eV}$

Question 8

If light of wavelength $600 \mathrm{~nm}$ is used to locate an electron to within one wavelength of the light, what is the minimum uncertainty in the electron's momentum?

A) $1.8 \times 10^{-32} \mathrm{~kg} \cdot \mathrm{m} / \mathrm{s}$
B) $1.8 \times 10^{-28} \mathrm{~kg} \cdot \mathrm{m} / \mathrm{s}$
C) $8.8 \times 10^{-29} \mathrm{~kg} \cdot \mathrm{m} / \mathrm{s}$
D) $1.1 \times 10^{-27} \mathrm{~kg} \cdot \mathrm{m} / \mathrm{s}$
E) $1.2 \times 10^{-32} \mathrm{~kg} \cdot \mathrm{m} / \mathrm{s}$

Question 9

If a particle in a box has a ground-state energy of $10.0 \mathrm{eV}$ , what is the energy of the fourth excited state?

A) $250 \mathrm{eV}$
B) $160 \mathrm{eV}$
C) $50.0 \mathrm{eV}$
D) $20.0 \mathrm{eV}$
E) $40.0 \mathrm{eV}$

Question 10

Which one of the following is true?

A) The electron spin quantum number can take on any one of four different values.
B) The principal quantum number of the electron in a hydrogen atom does not affect its energy.
C) The principal quantum number of an electron in the ground state is zero.
D) The orbital angular momentum quantum number of an electron state is always less than the principal quantum number.

Question 11

For an orbital angular momentum quantum number of 4 , what is the magnitude of the orbital angular momentum?

A) $3 \hbar$
B) $201 / 2 \hbar$
C) $61 / 2 \hbar$
D) $4 \hbar$
E) $12^{1 / 2 \hbar}$

Question 12

Except for helium, the outer subshell of a noble gas has what electronic configuration?

A) $\mathrm{d} 10$
B) $p^{6}$
C) $\mathrm{p}^{2}$
D) $\mathrm{s}^{1} \mathrm{p}^{4}$
E) $s^{2}$

Question 13

The configuration $1 \mathrm{~s}^{2} 2 \mathrm{~s} 22 \mathrm{p} 63 \mathrm{~s} 23 \mathrm{p} 1$ is for what element?

A) B
B) $\mathrm{Ne}$
C) $\mathrm{Al}$
D) $\mathrm{Cr}$
E) $\mathrm{F}$

Question 14

The Pauli exclusion principle

A) means that no two electrons in an atom can have the same orbit.
B) excludes electrons from atomic nuclei.
C) excludes protons from electron orbits.
D) implies that no two electrons in an atom can have identical sets of quantum numbers.

Question 15

What is the approximate average thermal energy of an electron in a solid at room temperature?

A) 0.00
B) $0.0010 \mathrm{eV}$
C) $0.025 \mathrm{eV}$
D) $1.0 \mathrm{keV}$
E) $27 \mathrm{eV}$

Question 16

A carbon dioxide laser emits photons of $10.6 \mu \mathrm{m}$ wavelength. How many photons per second are emitted by a $10.0 \mathrm{~kW} \mathrm{CO} 2$ laser?

A) $5.34 \times 1023$
B) $6.20 \times 1023$
C) $4.27 \times 10^{21}$
D) $5.39 \times 1030$
E) $3.17 \times 1018$

Question 17

A baseball has a mass of $0.15 \mathrm{~kg}$ . If pitched at $40.0 \mathrm{~m} / \mathrm{s}$ with a relative uncertainty of $1 \%$ , how uncertain is its position?

A) $1.1 \times 10^{-32} \mathrm{~m}$
B) $1.8 \times 10^{-33} \mathrm{~m}$
C) $1.1 \times 10^{-34} \mathrm{~m}$
D) $8.8 \times 10^{-34} \mathrm{~m}$

Question 18

The uncertainty in the position of a proton is $250 \mathrm{pm}$ . Estimate the kinetic energy of the proton.

A) $0.013 \mathrm{eV}$
B) $1.3 \times 10^{-23} \mathrm{eV}$
C) $0.24 \mathrm{eV}$
D) $100 \mathrm{MeV}$
E) $8.3 \times 10^{-5} \mathrm{eV}$

Question 19

The uncertainty in the position of a proton is $250 \mathrm{pm}$ . Estimate the velocity of the proton.

A) $130 \mathrm{~m} / \mathrm{s}$
B) $0.01 \mathrm{~m} / \mathrm{s}$
C) $1.6 \mathrm{~m} / \mathrm{s}$
D) $1.3 \times 10^{5} \mathrm{~m} / \mathrm{s}$
E) $1.6 \times 10^{3} \mathrm{~m} / \mathrm{s}$

Question 20

A beam of neutrons $\left(m=939.6 \mathrm{MeV} / \mathrm{c}^{2}\right.$ ) of momentum $12 \mathrm{keV} / \mathrm{c}$ is passed through a single slit of width 0.1 $\mathrm{nm}$ . As a result of this, the neutron beam acquires an uncertainty in the component of the momentum that is transverse to the beam direction. The distance between the slit and a screen onto which the neutrons are projected is $1.5 \mathrm{~m}$ . Using the uncertainty principle, estimate the expected width of the neutron distribution on the screen.

A) $0.1 \mathrm{~mm}$
B) $5 \mathrm{~m}$
C) $50 \mathrm{~cm}$
D) $1 \mathrm{~cm}$

Question 21

For the first excited state $(n=2)$ of the particle in a box of width $\mathrm{L}$ , what is the approximate uncertainty in momentum?

A) $3 \mathrm{~h} / \mathrm{L}$
B) $\mathrm{h} / 2 \mathrm{~L}$
C) $\mathrm{h} / \mathrm{L}$
D) $2 \mathrm{~h} / \mathrm{L}$

Question 22

How many electron states in the $\mathrm{H}$ atom have $\mathrm{n}=4$ and $\mathrm{l}=2$ ?

A) 10
B) 9
C) 6
D) 3
E) 5
F) 18