Physics Questions and Answers October 29, 2022

An ideal monoatomic gas is confined in a horizontal cylinder by a spring loaded piston (as shown in the figure). Initially the gas is at temperature T, pressure P and volume V, and the spring is in its relaxed state. The gas is then heated very slowly to temperature T2, pressure P and volume V. During this process the piston moves out by a

Light guidance in an optical fiber can be understood by considering a structure comprising of thin solid glass cylinder of refractive index n, surrounded by a medium of lower refractive index n. The light guidance in the structure takes place due to successive total internal reflections at the interface of the media n, and ny as shown in the

In a thin rectangular metallic strip a constant current I flows along the positive xdirection, as shown in the figure. The length, width and thickness of the strip are, w and d, respectively. A uniform magnetic field B is applied on the strip along the positive ydirection. Due to this, the charge carriers experience a net deflection along the z

For, k, I3 12, B0, For, , I3 12, B 1 , For, A, I3, 0, B 1 Then, the strangeness number of particle

An atomic spectral line is observed to split into twelve components due to Zeeman shift. If the lower state of the atom is 2P32, then the upper state will be

In an atom obeying LS coupling, the components of a spectral triplet state have separations 20 cm and 40 cm1 between the adjacent components. The term notation for this multiple is

In a ESR spectrum, the frequency of rotation for resonance condition for a free electron placed in a magnetic field of strength of 0.3 Tesla is O 7.5x108 Hz O 6.210 Hz 03.2106 Hz 8.4 x 106 Hz

A state is denoted by 4D52. The minimum number of electrons which could give rise to this state and a possible electronic configuration are, respectively.

Consider a HeNe laser with cavity lifetime te 6x108 sec. If reflectivitys of mirrors are R11.0 and R2 0.98, the cavity length d is equal to

In the LS coupling scheme, the terms arising from the two non equivalent delectrons are

For the P, level in the configuration of C12 atom, the Zeeman energy level shift in an external magnetic field of 0.1 Tesla is O0.07 cm 7.0 cm1 O0.12 cm O1.02 cm

The fundamental and first overtone frequencies of NO molecule are centered at 1876.06 cm and 3724.2 cm, respectively. The equilibrium vibration frequency and anharmonicity constant of NO molecule are, respectively 1876.06 cm and 7.33 x 102 7.33 x 102 and 1876.06 cm1 1903.98 cm and 7.33 x 10 O 1903.98 cm and 7.33 x 101

The diatomic molecule 1H35Cl has fundamental band in the vibrational spectra at 3.46 muon(micron). If the hydrogen is replaced by Deuterium (2H), the corresponding band for the molecule 2H35CI will be shifted by approximately.

The electromagnetic form factor F(g) of a nucleus is given by, F(q)e, where cis constant. Given that F(g)P(r)sin (gr)r dr with normalization condition p(r) 4xdr 1, where p(r) is charge den sity. The root mean square radius of the nucleus is given by 2c 03c 6c Oc3

For a system of two isospin 12 particles, the value of I1 , I2 in triplet and singlet states respectively are

The threshold kinetic energy of incident pi meson in the reaction pi PPPn for target proton at rest is equal to

The decay reactions 37S17 35Cl17 Beta Ve is.

The ground state of a nucleus has spinparity JP1. while the first excited state has JP3. The electro magnetic radiation emitted when the nucleus makes a transition from the first excited state to the ground state are.

A cyclotron with dees of radius 90 cm has a transverse magnetic field of 0.8 Tesla. The maximum kinetic energy to which a proton is accelerated is (Mass of proton 1.67 x 1027 kg).

The normalized ground state wave function of one electron atom 32 Zr is given by (r, 0,0) 12( 2 (2) e ao where the notations have usual meaning. Evaluate the probability of finding the electron at a distance greater than 2002. BUH 97, 2000

Q.

Show that the orbital angular momentum of the electron in hydrogen atom is L h (l1), where l is the orbital quantum number.

Q

Verify that the average value of for 1s electron in hydrogen atom is 1infinity.

Q1.

The ground state wave function of an electron in a hydrogen atom e where do is the radius of the innermost orbit. Verify 12 is given by (r) () BUH 97 that this wave function is normalized.

A helium atom (m 6.6465 x 1027 kg) moving at a speed of VHe 1.518 106 ms collides with an atom of nitro gen (m 2.3253 1026 kg) at rest. After the collision, the helium atom is found to be moving with a velocity of He 1.199 x 106 ms at an angle of 0e 78.75 rela tive to the direction of the original motion of the helium atom. (a) Find the

An atom of uranium (m 3.9529 1025 kg) at rest decays spontaneously into an atom of helium (m 6.6465 1027 kg) and an atom of thorium (m 3.8864 1025 kg). The helium atom is observed to move in the positive x direction with a velocity of 1.423 107 ms (Figure 1.2). (a) Find the velocity (magnitude and direc tion) of the thorium atom. (b) Find the

In one mole of a gas at a temperature of 650 K (kT 8.97 1021 J 0.0560 eV), calculate the number of molecules with energies between 0.0105 eV and 0.0135 eV. (b) In this gas, calculate the fraction of the molecules with energies in the range of 2.5 of the most probable energy (KT). N(E) (x 1025) N(E) (x 1025) 0.50 0.40 0.30 0.20 0.10 0.00 0.008

d) Forces of magnitude F_{I} =2 hat i -5 hat j +6 hat k , F 2 = - i +2 hat j - hat k and F_{3} =2 hat i +7 hat j acts on a particle P whose position vector is given by 4 hat i -3 hat j -2 hat k . Find the work done by the force in displace of the particle to the point O(6, 1, - 3)

A hydrogen atom (m = 1.674 10 ?27 kg) is moving with a velocity of 1.1250 10 7 m/s. It collides elastically with a helium atom (m = 6.646 10 ?27 kg) at rest. After the collision, the hydrogen atom is found to be moving with a velocity of ?6.724 10 6 m/s (in a direction opposite to its original motion). Find the velocity of the helium atom

A beam of helium3 atoms (m 3.016 u) is incident on a target of nitrogen14 atoms (m 14.003 u) at rest. During the collision, a proton from the helium3 nucleus passes to the nitrogen nucleus, so that following the collision there are two atoms an atom of heavy hydrogen (deuterium, m 2.014 u) and an atom of oxygen15 (m 15.003 u). The incident

An atom of beryllium (m 8.00 u) splits into two atoms of helium (m 4.00 u) with the release of 92.2 keV of energy. If the original beryllium atom is at rest, find the kinetic energies and speeds of the two helium atoms.

A 4.15volt battery is connected across a parallelplate capacitor. Illuminating the plates with ultraviolet light causes electrons to be emitted from the plates with a speed of 1.76 106 ms. (a) Suppose electrons are emitted near the center of the negative plate and travel perpendicular to that plate toward the opposite plate. Find the speed of the

A sample of argon gas is in a container at 35.0 C and 1.22 atm pressure. The radius of an argon atom (assumed spherical) is 0.710 100 m. Calculate the fraction of the container volume actually occupied by the atoms.

By differentiating the expression for the Maxwell Boltzmann energy distribution, show that the peak of the distribution occurs at an energy of 12KT.

A container holds N molecules of nitrogen gas at T = 280 K. Find the number of molecules with kinetic energies between 0.0300 eV and 0.0312 eV.

An atom of mass m m moving in the x direction with speed v v collides elastically with an atom of mass m2 3m at rest. After the collision the first atom moves in the y direction. Find the direction of motion of the second atom and the speeds of both atoms (in terms of v) after the collision.

A gas cylinder contains argon atoms (m 40.0 u). The tem perature is increased from 293 K (20C) to 373 K (100C). (a) What is the change in the average kinetic energy per atom (b) The container is resting on a table in the Earths gravity. Find the change in the vertical position of the con tainer that produces the same change in the average energy

For a molecule of O at room temperature (300 K), calculate the average angular velocity for rotations about the x or y axes. The distance between the O atoms in the molecule is 0.121 nm.

Calculate the fraction of the molecules in a gas that are moving with translational kinetic energies between 0.02kT and 0.04kT.

A villain with mass 80.0 kg runs at a velocity of 9.25 ms into Chuck Norris fist moving at a speed of 0.150 ms. The villain is knocked back at a velocity of 8.50 ms and angle 20.0 from the horizontal, while Chuck Norris fist moves at a velocity of 0.0745 ms and 10.0 from the horizontal. a. What is the mass of Chuck Norris fist in kg b. How much

The value of a for which the equation x ax10 and x ax 10 have a common root is 02 2 0 1

Find the value of ii i i .......i where i 1 50 01 01 O i1 Oi1

If TEMPLE is coded as VHQNIA. How would you code CHURCH OEKYWI OEKYQZD OEKYPZD O EKYQWD

The value of Oo 01 02 3 1 1 1 logy (xyz) logyz (xyz) log (xyz) is

For a back sale, Zara backed 2n more pies than Simran. Simran backed half as many pies as Mani, who baked n pies. No other pies were baked for the sale. What fraction of the total pies for sale did Mani bake O 1 16 8 16 O 13 16

Consider the following set of lines xy1. Area enclosed by them is 01 02 3 04

The total energy. E of an ideal nonrelativistic fermi gas in three dimensional is given by E PV the number of particles and Vis the volume of the gas. The value of is E N59 723 , where Nis

In the circuit of the figure, V, is 1Vww R 15V 15V www. R V Vout

A hydrogen atom in its ground state is collided with an electron of kinetic energy 12.97 eV. The maximum factor by which the radius of the atom would increase is

One mole of an ideal gas at 300K expands reversibly and isothermally from a pressure of 1.5x103 Nm to 5x102 Nm. The change in entropy (JK) of the universe is 00.21 0 19.1 O 0.21

The diode in the circuit given below has Vav 0.7 V but is ideal otherwise. The current (m mA) in the 4 ON resistor is 1 mA(T 0 0.5 0.4 0.6 2, 4 D 1 3

The translational operator (I) is defined as I f(x)f(xL), where f(x) in any arbitrary function of position x and L is any constant. If the position operator is represented by then the value of commutator OLX OLIL OLX 0

According to single particle nuclear shell model, the spin parity of first excited state of Be is 2 2 2

Consider the following functinos 1 1 X f(x). (x). 0

An unpolarized light propagating along zdirection is scattered from a clouds of charged particles (whose dimension is of the order of wavelength of light). The observer who is standing on the xaxis he will receive the state of polarization of the light is Oypolarized light Oxpolarized light zpolarized light circular polarized light

The rotational spectra of rigid diatomic molecule contains spectral lines separated by a distance 0.6cm1. The moment of inertia of the molecule will be O 9.3x104 kgm O 6.3x104kgm 9.3x106 kgm 6.3x106 kgm

The degeneracy of the spectral term D is 15 O 20 025 O 10

The following transformation Q Aq Bp. PCqDp is canonical under the condition O AD1 BC O AB1 CD O AC1 BD O AD1BC

A particle of mass m and velocity u collides elastically with a particle of mass 2m at rest. The maximum (up to two potential energy stored in the system during the collision is mu. The value of is decimal places).

21 A particle of mass m is subject to a force f(t) me N. The initial position and speed are 0. The distance covered by particle in two seconds is m. (Up to two decimal place) (given data e0.0183)

The ratio of nearest neighbours distance of SC crystal to FCC is (Round off to two decimal places)

The deBroglie wavelength of a nonrelativistic particle having a mass 900 MeVc and kinetic energy 2 MeV. is equal to x1014 m. (Upto two decimal place)

The spinorbit interaction in an sodium atom is given by H 21.5, where I and 5 denote the orbital and spin angular momenta of the electron, respectively. The splitting between the levels P32 and P2 (due to spinorbit inter action) is (Take fi 1) units (Your answer should be an integer)

Suppose a charge Q is distributed within a sphere of radius R in such a way that the charge density p(r) at a distance r from the centre of the sphere is 30 (Rr) p(r)R The value of n is for 0

A gold crystal has a FCC lattice with one gold atom per lattice point and a lattice constant of 4.08. Every gold atom has one valence electron. The fermi energy of the gold crystal is eV. (Answer upto two decimal places).

The entropy (S) of a thermodynamics system is give in terms of its internal energy (U) and volume (V) by SCU 44, where cis constant. The equation of state of the system is given by O 3PV 2U O4PV 3U 03PVU O 3PV 4U

Consider a system of 2 spinzero indistinguishable particles, each of which can occupy any of four lowest energy states of onedimensional infinite potential well. The number of microstates allowed to the system is,16 O 10 08 06

V ( A diode whose terminal characteristic are related as ID I, e and V is the thermal voltage ( 25 mV) is biased at Ip 2 mA. Its dynamic resistance is 25 ohms O 12.5 ohms 50 ohms O 100 ohms , where I, is the reverse saturation current

Match the following reactions on the left with the associated interactions on the right (1) PA k (A) strong (2) PyP n (B) electromagnetic (3) A 7 (C) weak (4) O 1A, 2B, 3C, 4C O 1A, 2B, 3D, 4D O 1A, 2B, 3C, 4D O1D, 2D, 3C, 4C (D) forbidden

The particular integral of the differential equation y 3y 2yeet is O ea e 2x 62 2x ex et

A small perturbation of the form H H, (a Bxx) is added to a potential V(x) (x). The first order correction to ground state energy for a particle of mass m bound in the potential will depend on O a, and y O a and B OB and y O a and y

A ball is thrown at with speed v at an angle of 45 with the horizontal inside a train moving forward with acceleration g. If the train is sufficiently high and long, the particle will momentarily be at rest at g V g2 g 2v 8 O The particle will never stop

Light is moving in a glass slab of refractive index n 3. If the glass slab is moving along (positive).xaxis of another frame S, with speed u, then the ratio of speed of light as viewed from the glass frame to that from the frame Sis, 0 1927 O 1729 O 2719 O 2917

Assuming that the diodes are ideal in figure, the currents in diodes isare SV 1kQ 1kQ ZD ZD 8V Current in D diode is 3 mA. Current in D diode is 6.5 mA. Current in D is 0 mA. Current in D is 8 mA.

State of a particle in an 1D infinite potential well of width L is given as following y(x) Asin COS 071 2mL 2 mL 2 L If the energy of the particle is measured, the possible values of energy will be 97 2mL 8 mL L where 0xL

In a scattering experiment, the particles are scattered from a spherically symmetric potential such that only swaves and pwaves are needed to be considered. Suppose the differential cross section can be written as do (0) dQ AB coseCcos (where A, B and Care constants) To find the value of the total cross section, which of the following values must

Which of the following statement(s) isare necessarily true for a n x n real matrix M, where I denotes its transpose OM M is symmetric. OMMT is antisymmetric. The eigenvalues of Mmust be real. If (p iq) is a complex eigenvalue, then (pig) will also be an eigenvalue of the matrix.

A wooden block performs SHM on a frictionless surface with frequency fo. The block carries a charge on its surface. If now a uniform electric field is switched ON as shown in figure, then the SHM of the block will be 16x moooooo of same frequency. with same mean position. with shifted mean position. of changed frequency.

A long solenoidal is carrying a time dependent current such that the magnetic field inside has the form B(t) Bot k, where k is along the axis of the solenoid. The displacement current at the point P on a circle of radius r in plane perpendicular to the axis is radially outward direction. is tangential to the loop. is inversely proportional to r.

The Lagrangian of a (three springs and two masses) system is given by 1 L mx mx kx k (x xj ) KX2 Where m 2m, m m, k 4k, k k and k 2k. The allowed frequencie(s) for small oscillation of the system isare O2k m 7k m 7k 2m HE

Consider two planets A and B with a mass ratio m mg 31 and a time period ratio of T TB 271, moving in an elliptical orbit around sun. IfE and a respectively denote energy and semimajor axis, then which of the following isare correct a a 91 a a 31 E E 13 DE E 31

A contract is to be completed in 46 days and 117 men were set to work, each working 8 hours a day. After 33 days, 47 of the work is completed. How many additional men may be employed so that the work may be completed in time, each man now working 9 hours a day O 61 071 081 072

If 4x 79, then the value of 4xx is 3 O 12. 12. 03 02 3 9 9

If ACNE is coded as 3, 7, 29, 11, then BOIL will be coded as O5, 31, 21, 25 O 5, 31, 19, 25 O5, 29, 19, 25 5, 29, 19, 27

Find total number of triangles in 11 12 O 14 13

A positronium atom is a system consisting of a positron and an electron revolving about their common centre of mass which lies half way between them. The ratio of velocity of electron in nth orbit of hydrogen atom to the velocity of electron in nth orbit of positronium. 011 012 21 41

For the ground electronic state of 12C 160 the potential energy curve is well approximated by a harmonic potential around the equilibrium inter nuclear distance. The curvature of this potential is approximately 2280 Jm. Then the frequency of fundamental absorption line of the molecule 71 THz 70 GHz 7.1 THz 0.71 THz

A hypothetical two dimensional crystal consisting of atoms arranged on a square grid is as shown in figure The reciprocal basis vectors can be written as The reciprocal basis vectors can be written as (ij) and (ij) a a i and j A a (ij) and (ij) a a OT i andj a a

In simple cubic crystal E versus krelation is given by E(k) Eoa4p cos (ka) cos (ka) cos (k.a) The difference between maximum and minimum energy is O 12 B 12 12 024 B

A homogeneous dielectric (s, 3) fills region1 (x 0) while region2 (x0) is free space. If ) 4 30 45 60 Zero 3, then the angle between electric field and normal to the interface in region2 is m

A particle moves in a circular orbit (shown in figure) which passes through O, under the influence of a central force directed towards point O. Point P is the position of the particle at any time t. The law of force is proportional to YA Or O D a P x 2a

The group of bits 10110111 is serially shifted (rightmost bit first) into an 8 bit parallel output shift register with an initial state 11110000. After three clock pulses, the register contains 10111000 10110110 11111110 O 01111111

The value of the limit, lim x0 is equal to 0 Opq P 9 ln (1 px) ln (1qx) X

If A, B are two quantum mechanical operators, such that A, B, then the commutator bracket 4, B can be written as O 2(ABBA) 4AB 0 O2(ABBA)

Consider the following matrix 1 1 41 1 1 The phase difference between the eigenvalues of the matrix A, will be 0 O 45 90 180

In an alpha decay ZX He 224 at rest, if Q is energy released, my, mg, and my are rest masses of the particles, then the velocity of alpha particle V, is given by 20m He my (mHe my) 20 my mHe (my mHe) 20 mHe (mHe my) 20 mHe my

What is the change of entropy involved in heating a gramatomic weight of silver at constant volume from 0 to 30 C. The value of C, over this temperature may be taken as a constant equal to 5.85 caldegmole,O 0.61 JK O 6.10 calK 0.61 calK O 6.10 JK

It is found for a simple magnetic system that if the temperature T is held constant and the magnetic field His changed to H AH. the entropy S changes by an amount A.S. AS CHAH T The magnetization M depends on the temperature as OM COM T T,M 2 COM T T

If in a rigid rotator of mass m, the energy of fourth excited is o, then energy of the first excited state is (in terms of so). 10. (Answer should be an integer)

In copper assuming that each atom contributes one free electron for conduction. Resistivity of copper is 1.7 x 106 ohmcm. Atomic weight 63.54 density 8.96 gmc.c. The mobility of electrons in copper is cnr voltsec. (Round off to one decimal place)

A body at rest spontaneously breaks up into two parts which move in opposite directions. The parts have rest masses of 3 kg and 5.33 kg and respective speeds of 0.8c and 0.6c. The rest mass of the original body is kg (up to two decimal places)