Physics Chapter 12 Quiz

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Questions and Answers

What is the total number of Na and Cl ions per unit cell of the NaCl crystal?

2 (correct)

What is the decimal sum of the binary numbers 10110.10, 11010.01, and 10101.11?

70.75 (correct)

70.25

69.50

70.50

Which matrix is both Hermitian and unitary?

(0 𝑖; 𝑖 0)

(0 -𝑖; 𝑖 0) (correct)

(1 -𝑖; 𝑖 1)

(0 1+𝑖; 1−𝑖 0)

What is the divergence of the vector $rac{ hat}{r^3}$?

$\frac{1}{r^4}$ Signup and view all the answers

Which statement accurately describes the magnitudes of spin magnetic moments?

$\mu_e < \mu_p < \mu_n$ Signup and view all the answers

How does a particle moving toward $x = 0$ behave according to the potential $V(x)$?

It approaches a maximum probability density. Signup and view all the answers

What is the significant characteristic of binary number addition shown here?

It requires carry bit for addition. Signup and view all the answers

Which property do the matrices in question 3 share?

They are all square matrices. Signup and view all the answers

What is the expression for the component of velocity along the line joining the source and the observer?

$\frac{1}{2 \sqrt{a^2 \sin^2(\omega t) + L^2}} \cdot a v_0 \sin(2\omega t)$ Signup and view all the answers

Under what condition is the observed frequency equal to f when the source is at positions $x = ±a$?

When the source is oscillating with maximum amplitude Signup and view all the answers

What is the correct work done when one mole of an ideal monoatomic gas is expanded isothermally from $V_0$ to $2.5V_0$?

$RT_0 \ln(2)$ Signup and view all the answers

When the process is isobaric, what is the change in internal energy for a monoatomic ideal gas expanded from $V_0$ to $2.5V_0$?

$\frac{9}{2}RT_0$ Signup and view all the answers

In a p-n junction diode, if the acceptor atoms in the p-side are more concentrated than the donor atoms in the n-side, what does this imply about the depletion width?

The depletion width in the p-side will be greater than in the n-side. Signup and view all the answers

What describes the internal energy change in an isothermal process of one mole of an ideal gas?

It is always equal to zero. Signup and view all the answers

What does the presence of depletion width indicate in a p-n junction diode?

The lack of free charge carriers in the junction region. Signup and view all the answers

What condition will result in the observed frequency f for the source located at x = 0?

The source must be stationary. Signup and view all the answers

What is the value of the line integral ∫𝑀 𝐸⃗.𝑑𝑙 along the path MCL given charges Q and 2Q?

0 V Signup and view all the answers

What is the magnetic field strength B inside the solenoid at a radius of 0.05m when the magnetic field is given as ⃗ (𝑡) = 𝐵0 sin 𝜔𝑡?

0.98 Weber/m2 Signup and view all the answers

What is the amplitude of the induced electric field at a distance of 0.07m from the axis of the solenoid?

0.49 V/m Signup and view all the answers

If the radius of the semicircle MCL is 2d and d is 10cm, what is the radius in meters?

0.2 m Signup and view all the answers

If the value of Q is 2C, what would be the force between the charges Q and 2Q at a distance of 2d?

6 N Signup and view all the answers

What is the least possible value of the air gap height d in a Newton’s rings experiment with a wavelength of 580nm?

290 Signup and view all the answers

In a retarding plate experiment with an incident wavelength of 600nm, what is the minimum thickness of the retarding plate for linearly polarized light?

3 Signup and view all the answers

What is the correct expression for the amplitude A of a 15.7mW laser beam with a diameter of 4mm?

35.4 Signup and view all the answers

Which of the following describes the interface between two linear dielectric media with relative permittivities 𝜀𝑟1 = 4 and 𝜀𝑟2 = 3, assuming no free charge at the interface?

The field will be continuous across the interface. Signup and view all the answers

If a muon is trapped in a potential well, which quantities correspond to the muon?

Eµ(x) and Ψµ(x) Signup and view all the answers

For a plano-convex lens used in the Newton's rings experiment, what feature is observed at the central fringe?

It is observed to be bright. Signup and view all the answers

What happens to linearly polarized light when it passes through a retarding plate?

It remains linearly polarized. Signup and view all the answers

What is the significance of the value of the angle of incidence when light interacts with a retarding plate?

It has no effect on the polarization state. Signup and view all the answers

What type of damping occurs in the spring-mass system when released from a position 0.5m from its equilibrium?

Underdamped Signup and view all the answers

Which equation represents the trajectory of the mass in the spring-mass system?

$y(t) = \frac{1}{2}(1 + t)e^{-4t}$ Signup and view all the answers

What is the maximum scattering wavelength ($\lambda'_{max}$) for γ-rays in the Compton scattering scenario?

0.098Å Signup and view all the answers

At what scattering angle does the maximum Compton shift ($\Delta\lambda$) occur for X-rays?

180° Signup and view all the answers

For a particle in a parabolic trajectory around a planet, what can be stated about its energy?

E > 0 Signup and view all the answers

What is the correct relationship for the angular momentum ($L$) of a particle with mass $m$ closest to the planet at distance $r_m$?

$L = \sqrt{2Gm^2M} r_m$ Signup and view all the answers

What type of frame of reference is 𝑆' when it is moving away from frame S with speed 𝑣?

Inertial frame Signup and view all the answers

What does the Compton shift ($\Delta\lambda$) represent?

Change in wavelength after scattering Signup and view all the answers

What is the total charge induced on the inner surface of a concentric spherical shell with a charge of -9C at the center, assuming a relative permittivity of 9?

-9.00 C Signup and view all the answers

What is the voltage drop across a 2kΩ resistance in a circuit with a Zener diode rated at 10V and a normal diode with a turn-on voltage of 0.7V?

10.0 V Signup and view all the answers

At 500K, which energy level corresponds to a probability of occupancy of 0.2, given the Fermi energy is 5.5eV?

6.00 eV Signup and view all the answers

What is the net change in entropy for one mole of an ideal monoatomic gas heated from 273K to 373K?

1.50 R Signup and view all the answers

For a simple cubic crystal, what is the smallest inter-planar spacing d that can be determined from its second order of diffraction with a wavelength of 1.32Å?

0.66 Å Signup and view all the answers

What is the calculated IC current in mA for the given transistor circuit with β = 100 and V_BE = 0.7V, under a V_CC of 15V?

10 mA Signup and view all the answers

How many moles of gas are heated in a closed container when the initial temperature is 273K and the final temperature is 373K?

1 mole Signup and view all the answers

How does the relative permittivity of a dielectric material affect the total charge involved in its electrostatic interaction with an external charge?

It modifies the electric field around the charge. Signup and view all the answers

Study Notes

Question 1

The total number of Na and Cl ions per unit cell of the NaCl crystal is 4

Question 2

The sum of the binary numbers 10110.10, 11010.01, and 10101.11, in decimal is 70.75

Question 3

This question asks which matrix is both Hermitian and unitary. The question provides multiple-choice options of matrices.

Question 4

The divergence of a 3-dimensional vector r/r³, where r is the unit radial vector, is zero.

Question 5

The magnitudes of spin magnetic moments of electron, proton, and neutron are μB, μN, and μN, respectively.

Question 6

This question describes a particle moving along the x-axis and approaching x = 0 from x = -∞, subjected to a potential V(x). The probability density P(x) of the particle for time t→∞ is shown in a figure. The correct option for the potential V(x) is presented as a multiple-choice graph.

Question 7

A plane electromagnetic wave is incident on an interface separating two media with refractive indices n₁ = 1.5 and n₂ = 2.0 at the Brewster angle θß. The angle a (in degrees) between the reflected and refracted wave is 90 degrees.

Question 8

The electric field of an electromagnetic wave is given by E = (4x + 3ŷ)ei(ωt + ax – 600y). The value of a is -450.

Question 9

A vector field F is expressed in cylindrical coordinates as F = s^A s^-B. If this represents an electrostatic field, then the possible values for A and B are 1 and 0, respectively.

Question 10

The trajectory y(x) = ax² + bx + c represents projectile motion in a uniform gravitational field. This is a possible trajectory.

Question 11

A crystal plane intercepts the principal axes a₁, a₂, and a₃ at 3a₁, 4a₂, and 2a₃, respectively. The Miller indices of the plane are (436).

Question 12

The number of atoms in the basis of a primitive hexagonal closed-packed structure is 2.

Question 13

The logic circuit's output Y is LOW when both A and B are LOW.

Question 14

The line integral for the vector v = 2xî + yz²ŷ + (3y + z²)ẑ along the closed path OABO is (3π-1)/7.

Question 15

In the x-y plane, a vector F(x,y) = xî – y î/ (x² + y²) is given. The magnitude of the flux of ∇ × F through a circular loop of radius 2, centered at the origin, is 2π.

Question 16

The roots of the polynomial f(z) = z⁴ – 8z³ + 27z² – 38z + 26 are z₁, z₂, z₃, and z₄. The statement Z₁+Z₂+Z₃+Z₄ = 19/4 is true.

Question 17

The ultraviolet catastrophe in classical cavity radiation theory arises from the assumption that the standing waves of all allowed frequencies in the cavity have the same average energy.

Question 18

Given the rest mass of an electron as 0.511MeV/c², the speed of an electron with kinetic energy 5.11MeV is closest to 0.996c.

Question 19

The ground state energy and wave function for an electron and a muon in a one-dimensional infinite square-well potential are given. Choose the correct option from among the provided graphs.

Question 20

In a Newton's rings experiment with free space wavelength 580nm, the least possible value for d is 290nm.

Question 21

Linearly polarized light of wavelength 600nm is normally incident on a retarding plate with n₁ = 1.5 and n₂ = 2.0. The minimum thickness of the plate is 2.

Question 22

A 15.7mW laser beam with a diameter of 4mm has an associated magnetic field amplitude of 100 A/m.

Question 23

The displacement vector D₂ in medium 2, given E₁ = (3x + 2y + 4z) and relative permittivities Er₁ = 4 and Er2 = 3, is (3x+6ŷ+8z)ɛ₀

Question 24

A water tank with a small hole has a jet that strikes the ground at a horizontal distance D. The maximum horizontal distance occurs when h₁ = h/2

Question 25

An incompressible fluid flows through a vertical pipe with cross-sectional area A₀. The volume flow rate from an individual hole in a mesh of area An at the bottom is n(A₀-Aₙ)√v² + 2gh

Question 26

A ball dropped from a height h with a coefficient of restitution e will take a time proportional to (1-e)/(1+e).

Question 27

The average time between successive collisions (tavg) of a gas atom in a cylinder-piston system is proportional to 1/√T

Question 28

For a gas of particles with three translational and three rotational degrees of freedom, Cp/Cv = 7/5

Question 29

Two traveling waves are superposed. For α=β=1, the resultant wave is a standing wave.

Question 30

For a dispersive medium with n(λ) = n₀ + a/λ², the group and phase velocities are the same when α = b/2√2

Question 31

A pure silicon crystal can be converted to an n-type crystal by doping with arsenic (As).

Question 32

In the OP-AMP circuit, the output vout is in-phase with the input Vin, and the gain is unity when R₁ = R₂.

Question 33

A spring-mass system is given. The motion will be underdamped.

Question 34

Compton scattering experiments with X-rays (λ = 1.024Å) and γ-rays (λ = 0.049Å) are described. For X-rays, (λ')max is observed at θ = 180°.

Question 35

A particle with energy E and angular momentum L is in a parabolic trajectory around a planet of mass M. The statement L = √2GMm²rm is true.

Question 36

Two events occur simultaneously in the S' frame. ∆t = 12.5 ns

Question 37

In the LCR AC circuit, the voltage VR and current I are in-phase at resonance frequency ω₀.

Question 38

In the P-V diagram of an engine, T₁T₃ = T₂T₄

Question 39

An oscillating whistle emits sound. The component of the velocity of the source along the line connecting the source to the observer is sin(2ωt)/2√(a²+L²)

Question 40

When one mole of an ideal monoatomic gas expands isothermally from volume V₁ to 2.5 V₁, the work done is RT ln(2.5).

Question 41

The depletion width in the n-side of a p-n junction diode is 0.18 µm.

Question 42

The Jacobian of the transformation u=2x+3y-z, v=x-4y+z, and w=x+y is -1.

Question 43

Two sides of the triangle are given as equations. Area of the triangle is 25.

Question 44

A particle slides down a frictionless inclined plane. The torque on the particle about point O is 5 N-m.

Question 45

The moment of inertia of a solid hemisphere about an axis through its center parallel to its flat surface is MR²/2. The distance from the center of mass is R√5/2

Question 46

A collimated light beam of intensity Io is normally incident on an air-dielectric interface with refractive index 2.0. The intensity of the reflected light is 0.16I₀.

Question 47

A charge of -9C placed at the center of a dielectric spherical shell induces a total charge of -3C on the inner surface.

Question 48

In a circuit with a Zener diode, a normal diode and a 2 kΩ resistor, the voltage drop across the 2kΩ resistor is 14.3V.

Question 49

The energy of a level with occupancy probability of 0.2 at 500K in a system with Fermi energy of 5.5eV is 5.77eV.

Question 50

When one mole of an ideal monoatomic gas is heated first from 273K to 303K, and then from 303K to 373K, the net change in entropy is 2.44R.

Question 51

For a simple cubic crystal, the smallest interplanar spacing that can be determined by second-order diffraction from monochromatic X-rays of wavelength 1.32 Å is 0.66 Å.

Question 52

The current Ic in the transistor circuit is 12.5 mA.

Question 53

The coefficient of x⁵ in the Taylor expansion of ex sin x around x = 0 is 0.000.

Question 54

The kinetic energy of 17O in the nuclear reaction is 7.3 MeV.

Question 55

The total energy of a 10kg satellite in circular orbit with speed 200m/s around a planet is 20 kJ

Question 56

For a multiple slit system with slits of 2µm width and 4µm period, illuminated by 600nm light, the maximum resolving power is 47.

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Test your understanding of key concepts from Physics Chapter 12, including topics like NaCl crystals, binary number addition, Hermitian matrices, and more. This quiz offers questions on fundamental physics principles and calculations relevant to the subject.