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Physics Questions and Answers September 19, 2022

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when light of a given wil i incident on a matellic surifice, the stopping pat for the photoelection 3.2 V. If a Ind light source whose W.L. is double that of the Ist source is used the stopping pot drops to 0.8 V. Calculate the W.L. of the Ist radiation the work fue cutt off free of the metal

An e et at rest producing three photons afte anihilating find the energy of II photon energy of 2 of the photons are 0 2 MeN 0.3 if L

Calculate the De Broglie Wavelength for ) a proton of Kinetic energy to men. (1) a 10 gm ball moving at goo msec (velocity).

Calculate the De Broglie wit for an e accelere to the pat difference V.

Calcultate the De boogle, Wil. for a material particle of mess in that is in thermal equili at temp T.

The speed of an e where DeBoogles Wit is equal to its compton Wil. (2) C (e) (b) (4)

Show that the De boogle W.1. associated with a particle of sest may mo KE Kis given. by ch JK (K 2mc)

Show that the phase velocity of Do Brogli wave avociated with a particle moving with relavistic spied (V) is greater than speed of light.

The dispersion relation of a certain wave is vjck m where was angular freg. of light KWave vector, cspee mo any constant. The group velocity I has the following propert k20 vc ask 300 U vc as W vc as ko VO ay 910 ju ko f Jo asko as Ko V.C

In a certain medium the war no. k. feq. w are related by the relation, (4( Hak) W where c a are constents if Ug is the group. velocity Up is the phane velacity then (a) Ug Up (b) Vp Vy (1 at ). (12ak) (c) uz upC (d) vgvp c (1 2ak

The relation buw angular frej us weve no. k fo AKBK given type of wave which the phase velocity () The group vedoeity ai () wave no. ko, for (6) 0 116100

1 The ang freg. of the surface wave in a liquid is given by w g k TK if g acceleration due to gravity P. density of liquid. T Surface tension 4 find the phase group velveity if 1. surface wave have very large W. 2. surface small 11.

Calculate the ground state energy for a linear harme osillator by using Heisenbery uncertainity pripcipl for Harmonic oscillator Dingo

Using the Heisenberg Uncertainity principle. Calces the min. possible energy of a particle of mass m moving in potno

Calculate the ground state energy of Hydrogen atom by using Heisenberg Uncertainity principle...

Armong the following physically acceptable (1) 3 sin X (3) 5x wave fucks which sep the ware five. (2) 41x1 Me dx

Which of the following ware fue zep accepta wave fue of the particle in the range th 00 x (a) AZO (b) B p(x) Alank (x) B CDs x (c) (x) cexp(D) (d) (x) Ex efx 2 9 seal CO 140 E, FO

Which of the wave fues shown in figure can n have physical significance in the interval show why A Y(x) TYD 4134 YOX) A JP(x) vises 911 (b). Date Foge No. x 30 breakdow

If the pookability that x. lies blue x f xf dx is p(x) dx a eax dx where 0

Consider a Dim particle which is confined withis the region osx a whose wave freer in this repon it izje iwt Calculat F 4(x, t) sin (1x) a the probability of finding the particle in the interval a x 30 4

The wavefunction of a spin12 particle is given by ) 2). Calculate the uncertainty of AS, (S) (S.). (2 points)

The wave fueen of a particle is given as 9(x) IxJ a Ja i) find the fooob. Of finding the particle a

The normalised state of a free particle is sep find a wave fue normalisation yix) Ne1 (kx constant,

The wave free of a particle at a certain insteint is given by 4(x) A exb x ikx If Pj k lz fa deno of the probabilities of finding the partile in the songe a to atda respectively. find the ratio P... za to 29tda fog P

A particle of mass m is confined in the I Dia box extending from 21 to 21 The wavef of the particle in this state is.,4(x) P cas (4) whine y is constant. (1) The normalization factor of this wave free is (B) FUL. X) TI (P) (a) A O.ft. (1) The expectation value of p in this state is 2 2 (B) 2 32 12 161 O (D) ha 82 .

Calcultate the expectation value of Pt p for wave free 4(x) () SinTT 0 0

Find the expectation value of position 4 mom. of a partile whose wode fuen is P(x) 2 tikk in all space. e Calculate

A free particle of mass in moves along the xdir at 0 then normalized wave fuer Of fue of the partice is given by the not dised 4(x,0) where is real const. 4. The expectation velue of mom in this state 42 (2 treyting exp 2x 1x 71x7 ,Fis (a) ha (6) h. JK (2) Th expectation (9) 142 24 m(2012) () (C) d value of the particle energy is 12 (421) ()

The wave fuck of a spinless particle of mass m in 1 Dim potential is 4(x) A exp(xx) carrelfanding to an Eigen value t both iN (X) is (9) 2E (1xx) 2xx (6) (d) 2 m 2 Eo (1xx) 2 E ( 1 2 x). The

The wave free of a particle moving in a i time independent pot V(x) iz P(x) exp (iaxb) where a 6 are const This means that the both voy is of the form a) V(x) of 2 (b) V(XC) of i (d) V(x) x e c) V(x) of O (e) V(x) Vo

for a particle of mass m in 1 Dim harmonie Lecillator bat V(x) mwx The first 2 ax excited energy eigen state is 4(x) x e The value of a is (B) (A) tawm 4h ) 35 (C) mw 271 (1) 201 3

The ground state (apart from namelisation) of partide. of whit mass moving in a 1 Dm pat v is exp(x) sh (2x) The pot Vix) is suital tinit so that t1 is (a) x (C) x 2 (B) Jax nh (x) x 2 () 2 x tan (2x) 2 2 1 2 x cathtvzx

A particle of mass m is represented by the w2. freen X(X) Aeikx where KA is the wave re A is constant. The magnitude of the probabil current density of the particle in 92 1A K (b) A1 DK. m 2.m 1C) 1A (hi) (d) 2 TAI (51.) 217

Calculate the prob. current donsity for a gomisial I have f packet 4 (x) A exp 1 i box 7

Calculate the prob. current. Been 4(a) A eikr density for a 3 dem ika

A bram of mono energetic particle having speed I is dilribed by the wave fee 4(x) u(x) e is seal free iks where u(x) This corresponds to current density. (a) ux) (b) (e) (d) U (2)

There are two toroidal solenoids having turns 400 and 100 respectively wound around the same form so that magnetic field of one passes through turn of another.Find the average flux through each turn of solenoid 1 if the current in solenoid 2 is 1.5 A.Also when the current in solenoid 1 is 2.5 A then average flux through each turn of solenoid 2 is

im I find the wave fier in wave vector space PK) for square wave packet 4o(x) Aeikox Aeikox, Ixlsa faccia) Txa (otherwise) fint the factor A so that 4(x) is normalised to unity. A

Suppose that the wave fie of a particle is gi by 4(x) Aeipox find the p(P).

given Suppose the wave fee of a partide at a insant is y(x) A cas k find the mom.. distribution fue (p). What are the possible valie of mem. in this state

2 The wave fue of a particle 4(x) (1) (2) (3) xe sketch the wave free (1) find (P) p(P) find the most probable value of mem 2 0

Consider a system whose initial state at t fis given in terms of a complete orthonamal set of 3 vectors as 1,2, , pz as H14 (,01 1 AP 103 3 I where A is real const. 12 find the value of A so that 4 (0)27 is nomalised to whity. 2) If the energies coresponding to 2, 1,2, are given by E, E2, Ez respectively. Write do the state of the

The Wave free of a particle at time t given by 4 (077 (1477 47) where 14,7 4 147 are the normalised eigen stati with eigen value E, E respectively with the come (E E). The shortest time after which 14()7 will become onthogonal to 4 (0)7 is ho (a) EE 2(EE) (5) Jihl EE E

The wave feer of a particle is given by y I tot where are the normalired eigen sta with chergies E. 4 E, corresponding to ground Ist excited state respectively. The expectation v of Hamiltonian in state i (a) to t.E. E 25 (1) 51 E 3 2

A particle in a doop square well patential extende from x0 to x L as a walle free Y(x) 19 212 where 182 1p, denote the ground state firs excited state fuc. The expectation value of SX) in this state is (b) b (9) L 2 L 2 64L 45 72 48L 972 (1) 2 48L 457

Consider a particle in a I Dim potential that sa the cond (V(x) V(x) je pot is symmetor Let 14.7 19,2 denate the ground Ist exi estate respectively. Let 42 9 407 04 be a normalised state with x. x being seal constants. The expectation value of x in this s Ey is given by 2 40x40 0, (4724,7 (0) (6) XX 424 4,12407 C) x (d) 22.0

1 Consider a particle of mass in subjected to an attoretive pot S (diracdelta) V(x) Vo f(x) V20 is in the case of ve energiy show that this particle has only one bouend state find the binding energy. 14 coresponding wave free 1) to the case of the energives Calculate the replation. I transmission cofficients. 1) What is the probability that

A particle in I Dim pat has the wave fuch where a is a const. Y(x) exp1x11 Ja a It follows that for a the const. Vo the both V(X) qual to 4 Vox (b) Vol2 (C) 1 S() (d) Vo 12

There are only one bound state for a particle of mass m in a 1 Dim bath well of the form showr in fejrere. The defth Vo satifies the cond, (14) 2778 97,22 (C) 2 ma2 812 mal 242 ma2

A particle in 2 Dim pot. 02 V(x) V o O 4 it oxd if If there is at least one bound state, the minime. depth of the path is a) 8m0 (6) 611 2mp (c) 25 me (d) 527 me2

g A partile of mass in is in the of sound the infinite square well. (x)f 1 COCK

Consider the states 14. 9ip2 . 10 1 2 w Calculate where 1 1 are orthonormal basis vectors. 1 4 2(x) (1) T8 (14 41) Fr (1xXx1) (IV) Ae 44 xx

6t satisfie b f and 1 a f (67) where the operator 6 bbt bb 1 1 Nbb selation N is also a operator. The eigen values of Nare (a) ve ve integers (6) All the integers. (C) 140 only. (d) 0 only

Calculate the expactation value of x as a ficer of time to ,A particle in the infinite pot well V(x) 0 ocx c.a otherwise 3 has the initial wave fuen, 4(x,0) A sin (TTX) osxa Determine the value of A so that y(x) is normales

f). f 1. E loev 22 E 3 ev,A particle is in the normalised state 142 which is in the superposition of energy eigen states E loev E 30 e1. The avery value the energy of the particle in the stal TR i.e. 4H4 20ev (EX. The state is given by 147 () loer x 5 ta 2 4 (b) (C) TE E E. ctoev 5 5 300K 1 1930ex 30 22 15 5 10 CV E30 ev 2

Consider a system whose initial state 140) hamiltonian H are given by 19(0) H 13 5 24 3 0 O 5 0 5 O O (1) If a measurment of energy is carried out. values will be obtain with what probabilitie (1) find the state of the system of any later tim Find the expectation value of th energy at t I at any latter time t. AL

Prove that for 2 operators A B ee 8 A8 Be B 31

A B are 2 operators sit, where AB x B show that B where a is a n. then

A particle of mass m is confined in the potential mwx V(x) x 0 Let the wieve free of the partile be given by 4, 4(x) JS 5 where Yo 4, are the eigen fues of ground state Ist excited state respectiily. The expectation value of energy is. (9) 31 he (b) 25 w (C.) 13 h (d) Il tw tw

Problem Let 10. 11) denate the normalized. eigen stater corresponding to the ground Ist excited state 1 Dim harmonic oscillator. The uncertanity sp in the state (10 1) is (a) 4 p hm2 Ap hmw (b) Ap hmw2 (d) sp 2h mw

A particle of mass m in 1 Dim moves in a potentic V(x) K (1eax) 2 where k a are the constants. If the partiles exicutes small oscillations around x0. Its Quantur, mechanical zero point energy. hk (b) k ma (e) tim k (d) hima k

Problem for a 1 Dim Harmonic oscillator show that (1.) (2)

In 1 Dim harmonie oscillator , 2.13 are the ground, Ist, Ind excited state respectively. There. three states are normalised orthogonal to one another. Y 4 are 2 states defined by 14 24, 34 17, 2 where x is car stant. 2 (1) The value of for which 1 is orthogonal to 4,, (a) 2 (b) 1 (ec) (c) 1 (d) 2 ( for the value of x. determined in (1) pant,

A particle is initially in the ground state in 1 dim harmonic oscillator pot V(x) 1 kx. If the spring cons il steddenly doubled. Calculate the probability of finding the particle in ground state of new pot..

the 1 A particle of mass m is in a cubic box of size a pot inside the box (o

If A Quantum particle of mass m mores in 2 dim in on. anharmonien oscillator potn V(x, y) 1 mwx 2 mwy 2 The energy eigen values are (n) is the integer or zero). 1.e. n 0,1,2,3, (a) kw (2n) (b). kw (n1), (c) 2w (n1) (1) hw(n)

The degeneracy of the state of energy En (n 1) where n is an integer (o or the integen) in a 2Dim isotropic Harmeni Oscillator, with path V(xy) mw (x y) (c) n1 (a) n(n1) 2 g) n(n1) (b) nint), 2 (f)(n1)(n2) 2 is (4)n1 (e))

Consider a spin less particle of mass m which it moving in a 3 dim potential V(x, y, z) Smwz , otherwise osewher (1) Write down the total enlyy total Wave feed for the nth state of the partile 2 2 Assuming that how 5 1h find the energies ma comesfonding degeneracies for the ground state Ist excited state

A linear harmonie oscillator is in. 14 22 60 1 1 , . 14 14, are eigen states of youvent Ist excited state respectively then expactation value of montum in this state 14 is (b) hmw (a) 0. (c) state hmw 2 hmw 4

The energy of the first excited quantumn stale of a particle in the potential vox, y) Imu(x4y) is a) 2w (c) 3 hw (b) 3 hw 2 (d) he

A Quantum partile of mass m is confined to a square region in xy plane, whose verticies are given by. (0,0),(1,0), (L, L) (0,L). Which of the following sep an... admissible wave fue of the particle (for I 71, n the integer) (b) sin(x) cos( nt) (1) (o) (74) sin (24). () sin (nux) co (MX4) L L (6) sin (m) sin (12)

Consicer a Quantum particle of mass m in a 3dim. Isotonic S.HO. potential V(x, y, z) 1 ( x 7 y 7z7) It is known that the particle is in an energy eigen state with eigen value Zhw. Which of the following can not be the worefice of the particle ( the particle ( mw Hnly) is th hermite polynomial Q (a) H (0x) exp(x (472)) (b) H (0.X) exp(x

find the expectation value of in the state 147, 14 111 11,0 11,17

Find the state Iem, find the expectation value of ophator if LxLy . Ly Lx 2.

D A system is known to be in a state described by the warefeed Y (0,) 12 5 1 6 30 Yem (0, p) are the spherical harmonies. The probabil of finding the system in a state with m0 is (b) 75 (c) 4 (a) Zeng (d) 115 13

A measuimment of zcomp of angmom. (2) i) made for a particle moving in the central pot with 84 21 4 400 (8) 34211 (0) 56 4211 (r) wave fue nem

Prob The Normalised wave free 4 4 corresponding ground state Ist excited state of a particle. You are given the information that the operator acts on the wave fue as 4 4, 4 4 () for 4 34 4Y a) 0.32 (b)0.32 (C) 0.75 (d) 6,() which of the following wave freentions are eigen fice of operator A (a) 4,442 (6) 1 not 4, () neither 4, nor (e)

for a spin particle, the expectation value of Sx Sy Sz where (Sx, Sy, Sy are spin operators) is ) (A.) th 8 (B.). i 3 8 (c) (5 16 16

skin particle is in the state expectation value of Sr, Sx, Sy Sy are, (A) (c) 0 12, 2 4. 5 2 1 0, 0 S th. The Sy Sy are given by

An e is in the state with spin wave fue 3 A is in the S depresentation, what is the probability of finding the 2component of its spin along the 2 dir.

Suppose a spin particle is in the state 12 What are the probabilities of 56 getting h 2comp of spin is measured. se comp of spin is measured. 2. If (ii) (i) Calculate the expectation value of Snie.

The wave feech of an e at a given tme es given by y f (80) 2 (9.X2. Calculate the exter average valus.. of zcomp of its magnetic moments.

The wave feed of an eat a f(x) 14 given time is f(x) 2X 3 X1 or f(r) 2173) calculate the expectation value of 2comp of magnetic (513) moment

For Pauli Spin operator, Probbe that (1) cior.n caso ion sino where o is any arbitrary angle. () eixox where a is any arbitoary angle. 2 (012 oy sin 2x M . T

The tamiltonian of an e in a constant mag field B. is given by H lo. B where it is the const. Pauli matrices. Let matix then the operator T (1T, 0, 03) denotes the W 1 I be 2x2 unit ti int et simplifies to a) I (as wt i .B. B b) I callet igB B () I sinut ig. B d) I Sin 2 wt sin ut sin wit coes wit B 1g. Be012111t e) I (04 2wt io B B . Sin

Let 147 denothe the ground state of 12 atom, Choos from given below, the correct statement () Lx, Ly 4 0 (6) J PZ. 0 () L 137 0 (d) Sx, Sy 74 0

The ground state wave free of H atom is given 4(0) where a is constant. () (b) 12 80 If Plr do is the probability of finding the e bw of rdr. tion P()0 at r 0. P() is maximum at r0 P(r) is maximum at r a P(xida dr

Calculate the expectation value of for single charged Helium ion in ground state. a

Positronium is an atom formed by an e and positron The mass of the position is same as that of cine and its charge is equal in magnitude but opposite in sign to that of an e. The positronium atom is thus similar to the H atom with the position replacing the proton. (1) The Binding energy of a positionium atom is (a) 13.6 ev (6) 6.8 ev (C) 27.2ev

are defined as 0 (f f) and Ty (ft f) i Que 10x and where Is are Paulispin matrices. And f., f obey anticom nutation relations, f f0, f f 1 then (b) 2ff1. (c) aff1 (d) ft f is given by ff1

Two identical fermions with spin 12 are placed in 1dir. box of length L. Eech particle has mass mn. The energy of the system is 13 11h. What is the space part of the wave for

Consider a. system of 3 noninteracting particles that are confined to move in a 1dim infinite pot well of length a defined as V(x) 0 , ocka otherwise 4 Determine the energy Wifeee of the ground, Ist exciti Int excited state when the particles are. spinless distinguishable (6) Gentical bosons (2) (e) spin half particles (1) distinguishable

For Paulis spis operators prove that, (G75) 2 ( 5 5 ) 3

Suppose you have an air column that is closed at one end, but the closing device can be moved back and forth to change the length of the air column. You place a vibrating tuning fork (f 330 Hz) at the open end of the column and set the length at one of the harmonics of this frequency. When listening to the tuning fork, how can you tell when you

the same 23) The electrostatic force between two objects with charge q1 and q2 depends on the electrostatic constant 1 4TEO where 0 8.85 1012 m is the permittivity constant associated with free space. N This value tells us the ability electric field lines are able to pass through a vacuum. Considering the units of the electrostatic constant,

To determine whether profitability of a firm is influenced by age of the manager, the following data was collected. If the envisaged model is PROFIT AGE 3AGE PROFI 3 2 1 2 7 1 T 0 1 5 1 6 AGE i. ii. 3 32 2 2 2 8 4 5 5 4 0 2 24 32 2 28 2 4 5 2 34 2 6 1 4 5 56 6 Find and interpret the relationship Compute and interpret the goodness of fit.

To find how variable P and G affect another variable Q the following cross sectional data was collected Q1 3 1 4 4 P1 3 1 2 GM i. 1 6 2 5 2 8 1 9 3 7 2 1 3 2 2 04 2 0 2 2 5 2 5 2 2 3 2 1 1 6 1 12 3 1 2 1 3 2 282 1 6 885 5 2 6 M F M F F M F M F F MF F M F If G is a slope dummy, compute and interpret the coefficients

The ground state energy for of 5 identical spin I particle which are subject to a 1 dem harmonie Oscilla or pot of freq. W is (b) 13 hw (c) tw (a) 15w 2 (d) 5hw

The unperturbed wavefied for the infinite square well is given by. Y(x) 2 Sin (ntx) a suppose we purturbed the system by simply raising the floor of the well by a constant amount only half way acroy. the well. Calculate the energy of the nth state greeting to first order. (

Calculate the energy of the nith excited state to first order perturbation theory for a spinless particle of mass n moving in an infinite potential, well of length 20 defined as, V(x) 0 8 () Vp(x (1) Vp(x) 7 PENEL which is modified at the bottom by the following pertiert ations, V. S(xL) AV. Sin TX 2L 0