QUESTION FOR SHORT ANSWER

ATOMIC PHYSICS

Q.1 In the photoelectric effect, why does the existence of a cutoff frequency speak in favour of the photontheory and against the wave theory?

Q.2 Explain the statement that one’s eyes could not detect faint starlight if light were not particle-like.

Q.3 How can a photon energy be given by E = hf when the very presence of the frequency f in the formulaimplies that light is a wave?

Q.4 The momentum p of a photon is given by p = h/. Why is it that c, the speed of light, does not appear inthis expression?

Q.5 Given that E = hf for a photon, the Doppler shift in frequency of radiation from a receding light sourcewould seem to indicate a reduced energy for the emitted photons. Is this in fact true? If so, what happenedto the conservation of energy principle?

Q.6 Any series of atomic hydrogen yet to be observed will probably be found in what region of the spectrum?

Q.7 Can a hydrogen atom absorb a photon whose energy exceeds its binding energy(13.6 eV)?

Q.8 Only a relatively small number of Balmer lines can be observed from laboratory discharge tubes, whereasa large number are observed in stellar spectra. Explain this in terms of the small density, high temperature,and large volume of gases in stellar atmospheres.

Q.9 What is the origin of the cutoff wavelength min

of figure shown? Why is it an important clue to the photonnature of x rays?

Q.10 Can atomic hydrogen be caused to emit x rays? If so, describe how. If not, why not?

Q.11 Why is it that Bohr theory, which does not work very well even for helium (Z = 2), gives such a goodaccount of the characteristic x-ray spectra of the elements, or at least of that portion that originates deepwithin the atom?

Q.12 The ionization potential of hydrogen is 13.6 V. Yet to obtain discharge in a cathode ray tube filled withhydrogen, a very high voltage ( ~104V) has to be applied across the tube. Explain this clearly. Alsoexplain why the gas must be at low pressure to obtain discharge.

Q.13 X-rays are produced when a fast electron hits a proper target. What happens to the electron?

Q.14 Why does the tail of a comet always point away from the sun?

Q.15 A neutron pion at rest decays into two gamma photons.0 +

Why cannot a single photon be born? What conservation law is in contradiction with it?

Q.16 What is so special about e/m rather than e end m separately?

Q.17 Why is it advisable to view a TV screen from a distance of about ten feet?

Q.18 The electrical conductivity of a gas increases when X-rays or -rays pass through it. Explain thisphenomenon.

Q.19 In photoelectric emission exchange of energy takes place among... (photon and electron/ photon, electronand lattice).

Q.20 The threshold frequencies for photoemission for three metals numbered 1,2,3 are respectively v1, v

2, v

3

and v1 > v

2 > v

3. An incident radiation of frequency v

0 > v

2 ... cause photoemission from 3 but... cause

photoemission from 1 (fill in the gaps with may, may not / will certainly).

NUCLEAR PHYSICS

Q.1 Why does the relative importance of the Coulomb force compared to the strong nuclear force increaseat large mass numbers?

Q.2 In your body, are there more neutrons than protons? More protons than electrons? Discuss

Q.3 Why is the binding energy per nucleon (see figure) low at low mass numbers? At high mass numbers?

Q.4 A radioactive nucleus can emit a positron, e+. This corresponds to a proton in the nucleus being converted to aneutron. The mass of a neutron, however, is greater than that of a proton. How then can positron emission occur?

Q.5 In beta decay the emitted electrons form a continuous spectrum, but in alpha decay the alpha particlesform a discrete spectrum. What difficulties did this cause in the explanation of beta decay, and how werethese difficulties finally overcome?

Q.6 How do neutrinos differ from photons? Each has zero charge and (presumably) zero rest mass andtravels at the speed of light.

Q.7 In radioactive dating with 238U, how do you get around the fact that you do not know how much 238Uwas present in the rocks to begin with? (Hint: What is the ultimate decay product of 238U?)

Q.8 If it is so much harder to get a nucleon out of a nucleus than to get an electron out of an atom, why try?

Q.9 In the generalized equation for the fission of 235U by thermal neutrons, 235U + n X + Y + bn, do youexpect the Q of the reaction to depend on the identity of X and Y?

Q.10 The half-life of 235U is 7.0 × 108 y. Discuss the assertion that if it had turned out to be shorter by a factorof 10 or so, there would not be any atomic bombs today.

Q.11 The binding energy curve of figure tells us that any nucleus more massive than A 56 can release energyby the fission process. Only very massive nuclides seem to do so, however. Why cannot lead, forexample, release energy by the fission process?

Q.12 Elements up to mass number 56 are created by thermonuclear fusion in the cores of stars. Why areheavier elements not also created by this process?

Q.13 Which would generate more radioactive waste products :- a fission reactor or a fusion reactor?

Q.14 How can Becquerel rays, i.e., the combination of -, - and -rays, be separated?

Q.15 When a nucleus undergoes -decay, is the product atom electrically neutral? In -decay?

Q.16 Experimental results in radioactivity show small variations from the results predicted by theory. Explainthis.

Q.17 If a nucleus emits only a -rays photon, does its mass number change? Does its mass change?

ONLY ONE OPTION IS CORRECT.Take approx. 2 minutes for answering each question.

Q.1 Let nr and nb be respectively the number of photons emitted by a red bulb and a blue bulb of equalpower in a given time.(A) nr = nb (B) nr < nb (C) nr > nb (D) data insufficient

Q.2 10–3 W of 5000 Å light is directed on a photoelectric cell. If the current in the cell is 0.16 A, thepercentage of incident photons which produce photoelectrons, is(A) 0.4% (B) .04% (C) 20% (D) 10%

Q.3 A proton and an electron are accelerated by same potential difference have de-Broglie wavelength pand e.(A) e = p (B)e < p (C) e > p (D) none of these.

Q.4 Two electrons are moving with the same speed v. One electron enters a region of uniform electric fieldwhile the other enters a region of uniform magnetic field, then after sometime if the de–Broglie wavelengthsof the two are 1 and 2, then:(A) 1 = 2 (B)1 > 2 (C) 1 < 2 (D) 1 > 2 or 1 < 2

Q.5 In a photo-emissive cell, with exciting wavelength , the maximum kinetic energy of electron is K. If the

exciting wavelength is changed to 4

3 the kinetic energy of the fastest emitted electron will be:

(A) 3K/4 (B) 4K/3 (C) less than 4K/3 (D) greater than 4K/3

Q.6 If the frequency of light in a photoelectric experiment is doubled, the stopping potential will(A) be doubled (B) halved(C) become more than doubled (D) become less than double

Q.7 An electron with initial kinetic energy of 100 eV is acceleration through a potential difference of 50 V.Now the de-Broglie wavelength of electron becomes

(A) 1 Å (B) 5.1 Å (C) 3 Å (D) 12.27 Å

Q.8 If h is Planck’s constant is SI system, the momentum of a photon of wavelength 0.01 Å is:(A) 10–2 h (B) h (C) 102 h (D) 1012 h

Q.9 The stopping potential for the photo electrons emitted from a metal surface of work function 1.7 eV is10.4 V. Identify the energy levels corresponding to the transitions in hydrogen atom which will result inemission of wavelength equal to that of incident radiation for the above photoelectric effect(A) n = 3 to 1 (B) n = 3 to 2 (C) n = 2 to 1 (D) n = 4 to 1

Q.10 When a photon of light collides with a metal surface, number of electrons, (if any) coming out is(A) only one (B) only two (C) infinite (D) depends upon factors

Q.11 Two radioactive material A1 and A2 have decay constants of 10 0 and 0. If initially they have samenumber of nuclei, the ratio of number of their undecayed nuclei will be (1/e) after a time

(A) 0

1

(B)09

1

(C) 010

1

(D) 1

Q.12 The frequency and the intensity of a beam of light falling on the surface of photoelectric material areincreased by a factor of two. This will :(A) increase the maximum energy of the photoelectrons, as well as photoelectric current by a factor oftwo.(B) increase the maximum kinetic energy of the photo electrons and would increase the photoelectriccurrent by a factor of two.(C) increase the maximum kinetic energy of the photoelectrons by a factor of greater than two and willhave no effect on the magnitude of photoelectric current produced.(D) not produce any effect on the kinetic energy of the emitted electrons but will increase the photoelectriccurrent by a factor of two.

Q.13 Light coming from a discharge tube filled with hydrogen falls on the cathode of the photoelectric cell. Thework function of the surface of cathode is 4eV. Which one of the following values of the anode voltage(in Volts) with respect to the cathode will likely to make the photo current zero.(A) – 4 (B) – 6 (C) – 8 (D) – 10

Q.14 A point source of ligth is used in a photoelectric effect. If the source is removed farther from the emittingmetal, the stopping potential :(A) will increase (B) will decrease(C) will remain constant (D) will either increase or decrease.

Q.15 A point source causes photoelectric effect from a small metal plate. Which of the following curves mayrepresent the saturation photocurrent as a function of the distance between the source and the metal ?

(A) (B) (C) (D)

Q.16 Let K1 be the maximum kinetic energy of photoelectrons emitted by a light of wavelength 1 and K2corresponding to 2. If 1 = 22 , then :

(A) 2K1 = K2 (B) K1 = 2K2 (C) K1 < 2

K2 (D) K1 > 2K2

Q.17 In a photoelectric experiment, the potential difference V that must be maintainedbetween the illuminated surface and the collector so as just to prevent any electronfrom reaching the collector is determined for different frequencies f of the incidentillumination. The graph obtained is shown.The maximum kinetic energy of the electrons emitted at frequency f1 is

(A) hf1 (B) )ff(

V

01

1

(C) h (f1 – f0) (D) eV1(f1 – f0)

Q.18 Radiation of two photon energies twice and five times the work function of metal are incident sucessively onthe metal surface. The ratio of the maximum velocity of photoelectrons emitted is the two cases will be(A) 1 :2 (B) 2 : 1 (C) 1 : 4 (D) 4 : 1

Q.19 Cut off potentials for a metal in photoelectric effect for light of wavelength 1, 2 and 3 is found to beV1, V2 and V3 volts if V1, V2 and V3 are in Arithmetic Progression and 1, 2 and 3 will be:(A) Arithmetic Progression (B) Geometric Progression(C) Harmonic Progression (D) None

Q.20 Photons with energy 5 eV are incident on a cathode C , on a photoelectric cell. The maximum energy ofthe emitted photoelectrons is 2 eV. When photons of energy 6 eV are incident on C, no photoelectronswill reach the anode A if the stopping potential of A relative to C is(A) 3 V (B) – 3V (C) – 1V (D) 4 V

Q.21 In a photoelectric experiment, the collector plate is at 2.0V with respect to the emitter plate made ofcopper = 4.5eV). The emitter is illuminated by a source of monochromatic light of wavelength 200nm.(A) the minimum kinetic energy of the photoelectrons reaching the collector is 0.(B) the maximum kinetic energy of the photoelectrons reaching the collector is 3.7eV.(C) if the polarity of the battery is reversed then answer to part A will be 0.(D) if the polarity of the battery is reversed then answer to part B will be 1.7eV.

Q.22 By increasing the intensity of incident light keeping frequency (v > v0) fixed on the surface of metal(A) kinetic energy of the photoelectrons increases(B) number of emitted electrons increases(C) kinetic energy and number of electrons increases(D) no effect

Q.23 In a photoelectric experiment, electrons are ejected from metals X and Y by light of intensity I andfrequency f. The potential difference V required to stop the electrons is measured for various frequencies.If Y has a greater work function than X ; which one of the following graphs best illustrates the expectedresults?

(A) (B) (C) (D)

Q.24 Monochromatic light with a frequency well above the cutoff frequency is incident on the emitter in aphotoelectric effect apparatus. The frequency of the light is then doubled while the intensity is keptconstant. How does this affect the photoelectric current?(A) The photoelectric current will increase.(B) The photoelectric current will decrease.(C) The photoelectric current will remain the same.(D) None of these

Q.25 In a hypothetical system a particle of mass m and charge –3q is moving around a very heavy particlehaving cahrge q. Assuming Bohr’s model to be true to this system, the orbital velocity of mass m when itis nearest to heavy particle is

(A)h2

q3

0

2

(B) h4

q3

0

2

(C) h2

q3

0(D) h4

q3

0

Q.26 de-Broglie wavelength of an electron in the nth Bohr orbit is n and the angular momentum is Jn, then:

(A) Jn n (B) n nJ

1(C) n

2nJ (D) none of these

Q.27 The angular momentum of an electron in the hydrogen atom is 2

h3. Here h is Planck’s constant. The

kinetic energy of this electron is:(A) 4.53 eV (B) 1.51 eV (C) 3.4 eV (D) 6.8 eV

Q.28 Consider the following electronic energy level diagram of H-atom:Photons associated with shortest and longest wavelengths would beemitted from the atom by the transitions labelled:(A) D and C respectively(B) C and A respectively(C) C and D respectively (D) A and C respectively

Q.29 In a hydrogen atom, the binding energy of the electron in the nth state is En, then the frquency of revolutionofthe electron in the nth orbits is:(A) 2En /nh (B) 2Enn/h (C) En/nh (D) Enn/h

Q.30 If the electron in a hydrogen atom were in the energy level with n = 3, how much energy in joule wouldbe required to ionise the atom? (Ionisation energy of H-atom is 2.18 × 10–18J):(A) 6.54 × 10–19 (B) 1.43 × 10–19 (C) 2.42 × 10–19 (D) 3.14 × 10–20

Q.31 In hydrogen and hydrogen like atoms, the ratio of difference of energies E4n–E2n and E2n–En varies withits atomic number z and n as:(A) z2 /n2 (B) z4/n4 (C) z / n (D) z0 n0

Q.32 In a hydrogen atom, the electron is in nth excited state. It may come down to second excited state byemitting ten different wavelengths. What is the value of n:(A) 6 (B) 7 (C) 8 (D) 5

Q.33 Difference between nth and (n +1)th Bohr’s radius of ‘H’ atom is equal to it’s (n–1)th Bohr’s radius. thevalue of n is:(A) 1 (B) 2 (C) 3 (D) 4

Q.34 An electron in hydrogen atom after absorbing energy photons can jump between energy states n1 andn2(n2 > n1). Then it may return to ground state after emitting six different wavelengths in emission spectrum.the energy of emitted photons is either equal to, less than or greater than the absorbed photons. Then n1and n2 are:(A) n2 = 4, n1 = 3 (B) n2 = 5, n1 =3 (C) n2 = 4, n1 = 2 (D) n2 = 4, n1 = 1

Q.35 The electron in a hydrogen atom makes transition from M shell to L. The ratio of magnitudes of initial tofinal centripetal acceleration of the electron is(A) 9 : 4 (B) 81 : 16 (C) 4 : 9 (D) 16 : 81

Q.36 The electron in a hydrogen atom makes a transition n1 n2 whose n1 and n2 are the principal quantumnumbers of the two states. Assume the Bohr model to be valid. The frequency of orbital motion of theelectron in the initial state is 1/27 of that in the final state. The possible values of n1 and n2 are(A) n1= 4, n2 = 2 (B) n1 = 3, n2 = 1 (C) n1 = 8, n2 = 1 (D) n1 = 6, n2 = 3

Q.37 The radius of Bohr’s first orbit is a0. The electron in nth orbit has a radius:(A) na0 (B) a0/n (C) n2a0 (D) a0/n

2

Q.38 The ionisation potential of hydrogen atom is 13.6 volt. The energy required to remove an electron fromthe second orbit of hydrogen is:(A) 3.4 eV (B) 6.8 eV (C) 13.6 eV (D) 27.2 eV

Q.39 Electron in a hydrogen atom is replaced by an identically charged particle muon with mass 207 times thatof electron. Now the radius of K shell will be(A) 2.56 × 10–3 Å (B) 109.7 Å (C) 1.21 × 10–3 Å (D) 22174.4 Å

Q.40 Monochromatic radiation of wavelength is incident on a hydrogen sample containing in ground state.Hydrogen atoms absorb the light and subsequently emit radiations of ten different wavelengths. Thevalue of is(A) 95 nm (B) 103 nm (C) 73 nm (D) 88 nm

Q.41 When a hydrogen atom, initially at rest emits, a photon resulting in transition n = 5 n = 1, its recoilspeed is about(A) 10–4 m/s (B) 2 × 10–2 m/s (C) 4.2 m/s (D) 3.8 × 10–2 m/s

Q.42 An electron collides with a fixed hydrogen atom in its ground state. Hydrogen atom gets excited and thecolliding electron loses all its kinetic energy. Consequently the hydrogen atom may emit a photoncorresponding to the largest wavelength of the Balmer series. The min. K.E.of colliding electron will be(A) 10.2 eV (B) 1.9 eV (C) 12.1 eV (D) 13.6 eV

Q.43 The frequency of revolution of electron in nth Bohr orbit is n. The graph between log n and log (n / 1)may be

(A) (B) (C) (D)

Q.44 Consider the spectral line resulting from the transition n = 2 n = 1 in the atoms and ions given below.The shortest wavelength is produced by :(A) hydrogen atom (B) deuterium atom(C) singly ionized helium (D) doubly ionized lithium

Q.45 In an atom, two electrons move around the nucleus in circular orbits of radii R and 4R. The ratio of thetime taken by them to complete one revolution is : (neglect electric interaction)(A) 1 : 4 (B) 4 : 1 (C) 1 : 8 (D) 8 : 1

Q.46 The electron in hydrogen atom in a sample is in nth excited state, then the number of different spectrumlines obtained in its emission spectrum will be :(A) 1 + 2 + 3 + ..........+(n – 1) (B) 1 + 2 + 3 + ....................+ ( n )(C) 1 + 2 + 3 + ..........+(n + 1) (D) 1 × 2 × 3 × ...................× (n – 1)

Q.47 The total energy of a hydrogen atom in its ground state is -13.6eV. If the potential energy in the firstexcited state is taken as zero then the total energy in the ground state will be :(A) -3.4eV (B) 3.4 eV (C) – 6.8eV (D) 6.8eV

Q.48 A neutron collides head on with a stationary hydrogen atom in ground state(A) If kinetic energy of the neutron is less than 13.6eV, collision must be elastic(B) if kinetic energy of the neutron is less than 13.6eV, collision may be inelastic.(C) inelastic collision takes place when initial kinetic energy of neutron is greater than 13.6eV.(D) perfectly inelastic collision cannot take place.

Q.49 The electron in a hydrogen atom make a transition from an excited state to the ground state. Which of thefollowing statement is true ?(A) Its kinetic energy increases and its potential and total energies decrease(B) Its kinetic energy decreases, potential energy increases and its total energy remains the same.(C) Its kinetic and toal energies decrease and its potential energy increases.(D) its kinetic potential and total energies decreases.

Q.50 The magnitude of angular momentum, orbit radius and frequency of revolution of electron in hydrogenatom corresponding to quantum number n are L, r and f respectively. Then according to Bohr's theory ofhydrogen atom,(A) fr2L is constant for all orbits (B) frL is constant for all orbits(C) f2rL is constant for all orbits (D) frL2 is constant for all orbits

Q.51 In a characteristic X– ray spectra of some atom superimposed oncontinuous X– ray spectra:(A) P represents K line(B) Q represents K line(C) Q and P represents K and K lines respectively (D) Relative positions of K and K depend on the particular atom

Q.52 The “K” X-rays emission line of tungsten occurs at = 0.021 nm. The energy difference between Kand L levels in this atom is about(A) 0.51 MeV (B) 1.2 MeV (C) 59 keV (D) 13.6 eV

Q.53 Consider the nuclear reactionX200 A110 + B90

If the binding energy per nucleon for X, A and B is 7.4 MeV, 8.2. MeV and 8.2 MeV respectively, whatis the energy released ?(A) 200 MeV (B) 160 MeV (C) 110 MeV (D) 90 MeV

Q.54 The binding energy per nucleon for C12 is 7.68 MeV and that for C13 is 7.5 MeV. The energy requiredto remove a neutron from C13 is(A) 5.34 MeV (B) 5.5 MeV (C) 9.5 MeV (D) 9.34 MeV

Q.55 The binding energies of nuclei X and Y are E1 and E2 respectively. Two atoms of X fuse to give one atomof Y and an energy Q is released. Then:(A) Q = 2E1–E2 (B) Q = E2–2E1 (C) Q = 2E1 + E2 (D) Q = 2E2 + E1

Q.56 Radius of the second Bohr obit of singly ionised helium atom is(A) 0.53 Å (B) 1.06 Å (C) 0.265 Å (D) 0.132 Å

Q.57 An electron in Bohr’s hydrogen atom has an energy of –3.4 eV. The angular momentum of the electron is(A) h / (B) h / 2(C) nh / 2 ( n is an integer) (D) 2h /

Q.58 If each fission in a U235 nucleus releases 200 MeV, how many fissions must occurs per second toproduce a power of 1 KW(A) 1.325 × 1013 (B) 3.125 × 1013 (C) 1.235 × 1013 (D) 2.135 × 1013

Q.59 The rest mass of the deuteron , 12 H , is equivalent to an energy of 1876 MeV, the rest mass of a proton

is equivalent to 939 MeV and that of a neutron to 940 MeV. A deuteron may disintegrate to a protonand a neutron if it :(A) emits a -ray photon of energy 2 MeV(B) captures a -ray photon of energy 2 MeV(C) emits a - ray photon of energy 3 MeV(D) captures a - ray photon of energy 3 MeV

Q.60 In an -decay the Kinetic energy of particle is 48 MeV and Q-value of the reaction is 50 MeV. Themass number of the mother nucleus is: (Assume that daughter nucleus is in ground state)(A) 96 (B) 100 (C) 104 (D) none of these

Q.61 In the uranium radioactive series the initial nucleus is 92U238, and the final nucleus is 82Pb206. When the

uranium nucleus decays to lead, the number of – particles emitted is.. and the number of -particlesemitted...(A) 6, 8 (B) 8, 6 (C) 16, 6 (D) 32, 12

Q.62 The radioactive sources A and B of half lives of 2 hr and 4 hr respectively, initially contain the samenumber of radioactive atoms. At the end of 2 hours, their rates of disintegration are in the ratio :

(A) 4 : 1 (B) 2 : 1 (C) 2 : 1 (D) 1 : 1

Q.63 In a RA element the fraction of initiated amount remaining after its mean life time is

(A) 1 – e

1(B) 2e

1(C)

e

1(D) 1– 2e

1

Q.64 90% of a radioactive sample is left undecayed after time t has elapsed. What percentage of the initialsamplewill decay in a total time 2t:(A) 20% (B) 19% (C) 40% (D) 38%

Q.65 A radioactive material of half-life T was produced in a nuclear reactor at different instants, the quantityproduced second time was twice of that produced first time. If now their present activities are A1 and A2respectively then their age difference equals:

(A) 2

1

A

Aln

2ln

T(B) T

2

1

A

Aln (C)

1

2

A2

Aln

2ln

T(D) T

1

2

A2

Aln

Q.66 Activity of a radioactive substance is R1 at time t1 and R2 at time t2(t2 > t1). Then the ratio 1

2

R

R is:

(A) 1

2

t

t(B) )tt( 21e (C) e

21 tt

(D) )tt( 21e

Q.67 There are two radionuclei A and B. A is an alpha emitter and B is a beta emitter. Their distintegrationconstants are in the ratio of 1 : 2. What should be the ratio of number of atoms of two at timet = 0 so that probabilities of getting and particles are same at time t = 0.(A) 2 : 1 (B) 1 : 2 (C) e (D) e–1

Q.68 The activity of a sample reduces from A0 to A0 / 3 in one hour. The activity after 3 hours more will be

(A) 33

A0(B)

9

A0 (C) 39

A0(D)

27

A0

Q.69 Half life of radium is 1620 years. How many radium nuclei decay in 5 hours in 5 gm radium? ( Atomicweight of radium = 223)(A) 9.1 × 1012 (B) 3.23 × 1015 (C) 1.72 × 1020 (D) 3.3 × 1017

Q.70 Half life for certain radioactive element is 5 min. Four nuclei of that element are observed at a certaininstant of time. After five minutesAssertion (A): It can be definitely said that two nuclei will be left undecayed.Reasoning (R): After half life i.e. 5 minutes, half of total nuclei will disintegrate. So only two nuclei willbe left undecayed. Then(A) A is correct & R is correct explanation of A.(B) Both are correct. But R is not correct explanation of A.(C) A is incorrect & R is correct.(D) Both are incorrect.

Q.71 A certain radioactive nuclide of mass number mx disintegrates, with the emission of an electron and radiation only, to give second nuclied of mass number my. Which one of the following equation correctlyrelates mx and my?(A) my = mx + 1 (B) my = mx – 2 (C) my = mx – 1 (D) my = mx

Q.72 The number of and emitted during the radioactive decay chain starting from Ra22688 and ending at

Pb20682 is(A) 3 & 6 (B) 4 & 5 (C) 5 & 4 (D) 6 & 6

Q.73 The activity of a sample of radioactive material is A1 at time t

1 and A

2 at time t

2 (t

2 >t

1). Its mean life is T.

(A) A1t1 = A

2t2

(B) A A

t t1 2

2 1

= constant(C) AA

2 = A

1 e t t T( )/1 2 (D) A2 = A

1 e t Tt( / )1 2

Q.74 A fraction f1 of a radioactive sample decays in one mean life, and a fraction f

2 decays in one halflife.

(A) f1 > f

2

(B) f1 < f

2

(C) f1 = f

2

(D) May be (A), (B) or (C) depending on the values of the mean life and half life

Q.75 A radioactive substance is being produced at a constant rate of 10 nuclei/s. The decay constant of thesubstance is 1/2 sec–1. After what time the number of radioactive nuclei will become 10? Initially thereare no nuclei present. Assume decay law holds for the sample.

(A) 2.45 sec (B) log (2) sec (C) 1.386 sec (D) )2(n

1

l sec

Q.76 The radioactivity of a sample is R1 at time T1 and R2 at time T2. If the half life of the specimen is T.Number of atoms that have disintegrated in time (T2 – T1) is proportional to(A) (R1T1 – R2T2) (B) (R1 – R2) T (C) (R1 – R2)/T (D) (R1 – R2) (T1 – T2)

Q.77 The decay constant of the end product of a radioactive series is (A) zero (B) infinite (C) finite (non zero) (D) depends on the end product.

Q.78 At time t = 0, N1 nuclei of decay constant

1 & N

2 nuclei of decay constant

2 are mixed . The decay

rate of the mixture is :

(A) t21eNN 21

(B) t21e

N

N

2

1

(C) tt 21 eNeN 2211 (D) N

1

1 N

2

2

t21e

ONE OR MORE THAN ONE OPTION MAY BE CORRECTTake approx. 3 minutes for answering each question.

Q.1 In photoelectric effect, stopping potential depends on(A) frequency of the incident light (B) intensity of the incident light by varies source distance(C) emitter’s properties (D) frequency and intensity of the incident light

Q.2 An electron in hydrogen atom first jumps from second excited state to first excited state and then, fromfirst excited state to ground state. Let the ratio of wavelength, momentum and energy of photons in thetwo cases be x, y and z, then select the wrong answer/(s) :(A) z = 1/x (B) x=9/4 (C) y=5/27 (D) z=5/27

Q.3 An electron is in an excited state in hydrogen-like atom. It has a total energy of –3.4 eV. If the kineticenergy of the electron is E and its de-Broglie wavelength is , then(A) E = 6.8 eV, = 6.6 × 10–10 m (B) E = 3.4 eV, = 6.6 × 10–10 m(C) E = 3.4 eV, = 6.6 × 10–11 m (D) E = 6.8 eV, = 6.6 × 10–11 m

Q.4 A particular hydrogen like atom has its ground state binding “energy 122.4eV. Its is in ground state.Then:(A) Its atomic number is 3(B) An electron of 90eV can excite it.(C) An electron of kinetic energy nearly 91.8eV can be brought to almost rest by this atom.(D) An electron of kinetic energy 2.6eV may emerge from the atom when electron of kinetic energy

125eV collides with this atom.

Q.5 A beam ofultraviolet light of all wavelengths passes through hydrogen gas at room temperature, in thex-direction. Assume that all photons emitted due to electron transition inside the gas emerge in they-direction. Let A and B denote the lights emerging from the gas in the x and y directions respectively.(A) Some of the incident wavelengths will be absent in A.(B) Only those wavelengths will be present in B which are absent in A.(C) B will contain some visible light.(D) B will contain some infrared light.

Q.6 If radiation of allow wavelengths from ultraviolet to infrared is passed through hydrogen agas at roomtemperature, absorption lines will be observed in the :(A) Lyman series (B) Balmer series (C) both (A) and (B) (D) neither (A) nor (B)

Q.7 In the hydrogen atom, if the reference level of potential energy is assumed to be zero at the ground statelevel. Choose the incorrect statement.(A) The total energy of the shell increases with increase in the value of n(B) The total energy of the shell decrease with increase in the value of n.(C) The difference in total energy of any two shells remains the same.(D) The total energy at the ground state becomes 13.6 eV.

Q.8 Choose the correct statement(s) for hydrogen and deuterium atoms (considering motion of nucleus)(A) The radius of first Bohr orbit of deuterium is less than that of hydrogen(B) The speed of electron in the first Bohr orbit of deuterium is more than that of hydrogen.(C) The wavelength of first Balmer line of deuterium is more than that of hydrogen(D) The angular momentum of electron in the first Bohr orbit of deuterium is more than that of hydrogen.

Q.9 Let An be the area enclosed by the nth orbit in a hydrogen atom. The graph of ln (An/A1) agains ln (n).(A) will pass through origin(B) will be a stright line will slope 4(C) will be a monotonically increasing nonlinear curve(D) will be a circle.

Q.10 A neutron collides head-on with a stationary hydrogen atom in ground state. Which of the followingstatements are correct (Assume that the hydrogen atom and neutron has same mass) :(A) If kinetic energy of the neutron is less than 20.4 eV collision must be elastic.(B) If kinetic energy of the neutron is less than 20.4 eV collision may be inelastic.(C) Inelastic collision may be take place only when initial kinetic energy of neutron is greater than 20.4 eV.(D) Perfectly inelastic collision can not take place.

Q.11 When a nucleus with atomic number Z and mass number A undergoes a radioactive decay process:(A) both Z and A will decrease, if the process is decay(B) Z will decrease but A will not change, if the process is + decay(C) Z will decrease but A will not change, if the process is – decay(D) Z and A will remain unchanged, if the process is decay.

Q.12 In a Coolidge tube experiment, the minimum wavelength of the continuous X-ray spectrum is equal to66.3 pm, then(A) electrons accelerate through a potential difference of 12.75 kV in the Coolidge tube(B) electrons accelerate through a potential difference of 18.75 kV in the Coolidge tube(C) de-Broglie wavelength of the electrons reaching the anticathode is of the order of 10m.(D) de-Broglie wavelength of the electrons reaching the anticathode is 0.01Å.

Q.13 The potential difference applied to an X-ray tube is increased. As a result, in the emitted radiation:(A) the intensity increases (B) the minimum wave length increases(C) the intensity decreases (D) the minimum wave length decreases

Q.14 When the atomic number A of the nucleus increases(A) initially the neutronproton ratio is constant = 1(B) initially neutronproton ratio increases and later decreases(C) initially binding energy per nucleon increases and later decreases(D) the binding energy per nucleon increases when the neutronproton ratio increases.

Q.15 Let mp be the mass of a proton, mn the mass of a neutron, M1 the mas of a Ne2010 nucleus and M2 the

mass of a Ca4020 nucleus. Then

(A) M2 = 2M1 (B) M2 > 2M1 (C) M2 < 2M1 (D) M1 < 10(mn + mp)

Q.16 The decay constant of a radio active substance is 0.173 (years)–1. Therefore :(A) Nearly 63% of the radioactive substance will decay in (1/0.173) year.(B) half life of the radio active substance is (1/0.173) year.(C) one -forth of the radioactive substance will be left after nearly 8 years.(D) all the above statements are true.

ANSWER KEY

ONLY ONE OPTION IS CORRECT.

Q.1 C Q.2 B Q.3 C Q.4 D Q.5 D Q.6 C Q.7 A

Q.8 D Q.9 A Q.10 A Q.11 B Q.12 C Q.13 D Q.14 C

Q.15 D Q.16 C Q.17 C Q.18 A Q.19 C Q.20 B Q.21 B

Q.22 B Q.23 A Q.24 B Q.25 A Q.26 A Q.27 B Q.28 C

Q.29 A Q.30 C Q.31 D Q.32 A Q.33 D Q.34 C Q.35 D

Q.36 B Q.37 C Q.38 A Q.39 A Q.40 A Q.41 C Q.42 C

Q.43 C Q.44 D Q.45 C Q.46 B Q.47 C Q.48 A Q.49 A

Q.50 B Q.51 C Q.52 C Q.53 B Q.54 A Q.55 B Q.56 B

Q.57 A Q.58 B Q.59 D Q.60 B Q.61 B Q.62 C Q.63 C

Q.64 B Q.65 C Q.66 D Q.67 A Q.68 B Q.69 B Q.70 D

Q.71 D Q.72 C Q.73 C Q.74 A Q.75 C Q.76 B Q.77 A

Q.78 C

ONE OR MORE THAN ONE OPTION MAY BE CORRECT

Q.1 A,C Q.2 B Q.3 B Q.4 A,C,D

Q.5 A,C,D Q.6 A Q.7 B Q.8 A

Q.9 A,B Q.10 A,C Q.11 A,B,D Q.12 B

Q.13 A,D Q.14 A,C Q.15 C,D Q.16 A,C