Modern Physics is one of the scoring topics in IIT-JEE. So, make sure that you revise this topic through these important questions!

**Q.1** A parallel beam of uniform, monochromatic light of wavelength 2640 A has an intensity of 200W/m^{2} . The number of photons in 1mm^{3} of this radiation are ….

**Q.2** When photons of energy 4.25eV strike the surface of a metal A, the ejected photoelectrons have maximum kinetic energy T_{a} eV and de Broglie wavelength λ_{a} . The maximum kinetic energy of photoelectrons liberated from another metal B by photons of energy 4.7eV is T_{b} = (T_{a} – 1.5) eV. If the De Broglie wavelength of these photoelectrons is λ_{b} = 2λ_{a} then find

**(a)** The work function of a** (b)** The work function of b is **(c)** T_{a} and T_{b}

**Q.3** When a monochromatic point source of light is at a distance of 0.2 m from a photoelectric cell, the cut off voltage and the saturation current are respectively 0.6 volt and 18.0 mA. If the same source is placed 0.6 m away from the photoelectric cell, then find

** (a)** the stopping potential

** (b)** the saturation current

**Q.4** An isolated metal body is illuminated with monochromatic light and is observed to become charged to a steady positive potential 1.0 V with respect to the surrounding. The work function of the metal is 3.0 eV. The frequency of the incident light is ………….

**Q.5** 663 mW of light from a 540 nm source is incident on the surface of a metal. If only 1 of each 5 × 10^{9} incident photons is absorbed and causes an electron to be ejected from the surface, the total photocurrent in the circuit is

**Q.6** Light of wavelength 330 nm falling on a piece of metal ejects electrons with sufficient energy which requires voltage V_{0} to prevent a collector. In the same setup, light of wavelength 220 nm, ejects electrons which require twice the voltage V_{0} to stop them in reaching a collector. Find the numerical value of voltage V_{0} .(Take plank’s constant, h = 6.6 × 10^{–34} Js and 1 eV = 1.6 × 10^{–19} J)

**Q.7** A hydrogen atom in a state having a binding energy 0.85eV makes a transition to a state of excitation energy 10.2eV. The wave length of emitted photon is ……….nm.

**Q.8** A hydrogen atom is in 5^{th} excited state. When the electron jumps to ground state the velocity of recoiling hydrogen atom is ………..m/s and the energy of the photon is ………eV.

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** Q.9** The ratio of series limit wavelength of Balmer series to wavelength of first line of paschen series is ……….

**Q.10** An electron joins a helium nucleus to form a He+ ion. The wavelength of the photon emitted in this process if the electron is assumed to have had no kinetic energy when it combines with nucleus is ………nm.

**Q.11** Three energy levels of an atom are shown in the figure. The wavelength corresponding to three possible transition are λ_{1} , λ_{2} , and λ_{3} . . The value of λ_{1} and λ_{2} is given by …..

**Q.12** Imagine an atom made up of a proton and a hypothetical particle of double the mass of an electron but having the same charge as the electron. Apply the Bohr atom model and consider a possible transitions of this hypothetical particle to the first excited level. Find the longest wavelngth photon that will be emitted λ (in terms of the Rydberg constant R.)

**Q.13** In a hydrogen atom, the electron moves in an orbit of radius 0.5 Å making 1016 revolution per second. The magnetic moment associated with the orbital motion of the electron is ……

**Q.14** The positron is a fundamental particle with the same mass as that of the electron and with a charge equal to that of an electron but of opposite sign. When a positron and an electron collide, they may annihilate each other. The energy corresponding to their mass appears in two photons of equal energy. Find the wavelength of the radiation emitted.

^{2})MeV and hC = 1.2×10

^{–12}MeV.m where h is the Plank’s constant and C is the velocity of light in air]

**Q.15** A small 10W source of ultraviolet light of wavelength 99 nm is held at a distance 0.1 m from a metal surface. The radius of an atom of the metal is approximately 0.05 nm. Find

** (i)** the average number of photons striking an atom per second.

**(ii)** the number of photoelectrons emitted per unit area per second if the efficiency of liberation of photoelectrons is 1%.

**Q.16** The surface of cesium is illuminated with monochromatic light of various wavelengths and the stopping potentials for the wavelengths are measured. The results of this experiment is plotted as shown in the figure. Estimate the value of work function of the cesium and Planck’s constant

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**Q.17** A hydrogen like atom has its single electron orbiting around its stationary nucleus. The energy to excite the electron from the second Bohr orbit to the third Bohr orbit is 47.2 eV. The atomic number of this nucleus is…

**Q.18** A single electron orbits a stationary nucleus of charge Ze where Z is a constant and e is the electronic charge. It requires 47.2eV to excite the electron from the 2nd Bohr orbit to 3rd Bohr orbit. Find

**(i)** the value of Z,

**(ii)** energy required to excite the electron from the third to the fourth orbit

**(iii)** the wavelength of radiation required to remove the electron from the first orbit to infinity

**(iv)** the kinetic energy, potential energy and angular momentum in the first Bohr orbit

**(v)** the radius of the first Bohr orbit.

**Q.19** A hydrogen like atom (atomic number Z) is in higher excited state of quantum number n. This excited atom can make a transition to the first excited state by successively emitting two photons of energy 22.95eV and 5.15eV respectively. Alternatively, the atom from the same excited state can make transition to the second excited state by successively emitting two photons of energies 2.4eV and 8.7eV respectively. Find the values of n and Z.

**Q.20** Find the binding energy of an electron in the ground state of a hydrogen like atom in whose spectrum the third of the corresponding Balmer series is equal to 108.5nm.

** Q.21** Which level of the doubly ionized lithium has the same energy as the ground state energy of the hydrogen atom. Find the ratio of the two radii of corresponding orbits.

**Q.22** The binding energies per nucleon for deuteron (_{1}H^{2} ) and helium (_{2}He^{4} ) are 1.1 MeV and 7.0 MeV respectively. The energy released when two deuterons fuse to form a helium nucleus (_{2}He^{4} ) is …..

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**Q23. **A monochromatic point source S radiating wavelength 6000 Å with power 2 watt, an aperture A of diameter 0.1 m & a large screen SC are placed as shown in figure . A photoemissive detector D of surface area 0.5 cm2 is placed at the centre of the screen. The efficiency of the detector for the photoelectron generation per incident photon is 0.9.

**(i)** Calculate the photon flux density at the centre of the screen and the photocurrent in the detector .

** (ii)** If a concave lens L of focal length 0.6 m is inserted in the aperture as shown, find the new values of photon flux density & photocurrent Assume a uniform average transmission of 80% for the lens .

**(iii)** If the work-function of the photoemissive surface is 1 eV, calculate the values of the stopping potential in the two cases (without & with the lens in the aperture).

**Q.24** A gas of identical hydrogen like atoms has some atoms in the lowest (ground) energy level A & some atoms in a particular upper (excited) energy level B & there are no atoms in any other energy level. The atoms of the gas make transition to a higher energy level by the absorbing monochromatic light of photon energy 2.7eV. Subsequently, the atoms emit radiation of only six different photon energies. Some of the emitted photons have energy 2.7 eV. Some have energy more and some have less than 2.7 eV.

**(i)** Find the principal quantum number of the initially excited level B.

**(ii)** Find the ionisation energy for the gas atoms.

**(iii)** Find the maximum and the minimum energies of the emitted photons.

**Q.25** Simplified picture of electron energy levels in a certain atom is shown in the figure. The atom is bombarded with high energy electrons. The impact of one of these electron has caused the complete removal of K-level is filled by an electron from the L-level with a certain amount of energy being released during the transition. This energy may appear as X-ray or may all be used to eject an M-level electron from the atom.

**Find : (i)** the minimum potential difference through which electron may be accelerated from rest to cause the ejectrion of K-level electron from the atom.

**(ii)** energy released when L-level electron moves to fill the vacancy in the K-level.

**(iii)** wavelength of the X-ray emitted.

** (iv)** K.E. of the electron emitted from the M-level.

**Q.26** A small bottle contains powdered beryllium Be & gaseous radon which is used as a source of α- particles. Neutrons are produced when α- particles of the radon react with beryllium. The yield of this reaction is (1/ 4000) i.e. only one α- particle out of 4000 induces the reaction. Find the amount of radon (Rn^{222}) originally introduced into the source, if it produces 1.2 × 10^{6} neutrons per second after 7.6 days. [T_{1/2} of R_{n} = 3.8 days]

**Q.27** An experiment is done to determine the half – life of radioactive substance that emits one β- particle for each decay process. Measurement show that an average of 8.4 β are emitted each second by 2.5 mg of the substance. The atomic weight of the substance is 230. Find the half life of the substance.

**Q.28** A wooden piece of great antiquity weighs 50 gm and shows C^{14} activity of 320 disintegrations per minute. Estimate the length of the time which has elapsed since this wood was part of living tree, assuming that living plants show a C^{14} activity of 12 disintegrations per minute per gm. The half life of C^{14} is 5730 yrs

**Q.29** A radionuclide with disintegration constant λ is produced in a reactor at a constant rate α nuclei per sec. During each decay energy E_{0} is released. 20% of this energy is utilised in increasing the temperature of water. Find the increase in temperature of m mass of water in time t. Specific heat of water is S. Assume that there is no loss of energy through water surface.

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**Q.30** A hydrogen like atom (atomic number Z) is in a higher excited state of quantum number n. This excited atom can make a transition to the first excited state by successively emitting two photons of energies 10.20 eV & 17.00 eV respectively. Alternatively, the atom from the same excited state can make a transition to the second excited state by successively emitting two photons of energies 4.25 eV & 5.95 eV respectively. Determine the values of n & Z. (Ionisation energy of hydrogen atom = 13.6 eV) **[JEE’94]**

**Q.31** In a photo electric effect set-up, a point source of light of power 3.2 × 10^{-3} W emits mono energetic photons of energy 5.0 eV. The source is located at a distance of 0.8 m from the centre of a stationary metallic sphere of work function 3.0 eV & of radius 8.0 × 10^{-3}m . The efficiency of photo electrons emission is one for every 10^{6} incident photons. Assume that the sphere is isolated and initially neutral, and that photo electrons are instantly swept away after emission.

**(a)** Calculate the number of photo electrons emitted per second.

**(b)** Find the ratio of the wavelength of incident light to the De – Broglie wave length of the fastest photo electrons emitted. **(c)** It is observed that the photo electron emission stops at a certain time t after the light source is switched on. Why ?

**(d)** Evaluate the time t. ** [JEE’95]**

**Q.32** An electron in the ground state of hydrogen atoms is revolving in anti-clockwise direction in a circular orbit of radius R.

**(i)** Obtain an expression for the orbital magnetic dipole moment of the electron.

**(ii)** The atom is placed in a uniform magnetic induction, such that the plane normal to the electron orbit make an angle of 30º with the magnetic induction. Find the torque experienced by the orbiting electron. **[JEE’96]**

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**Q.33** A potential difference of 20 KV is applied across an x-ray tube. The minimum wave length of X – rays generated is ________ . ** [JEE’96]**

**Q.34** Photoelectrons are emitted when 400 nm radiation is incident on a surface of work function 1.9eV. These photoelectrons pass through a region containing α-particles. A maximum energy electron combines with an α-particle to form a He^{+} ion, emitting a single photon in this process. He^{+} ions thus formed are in their fourth excited state. Find the energies in eV of the photons, lying in the 2 to 4eV range, that are likely to be emitted during and after the combination. [Take , h = 4.14 x 10^{-15} eV -s ] ** [JEE ’99]**

**Q.35(a)** Imagine an atom made up of a proton and a hypothetical particle of double the mass of the electron but having the same charge as the electron. Apply the Bohr atom model and consider all possible transitions of this hypothetical particle to the first excited level. The longest wavelength photon that will be emitted has wavelength λ (given in terms of the Rydberg constant R for the hydrogen atom) equal to

**(A)** 9/(5R) ** (B)** 36/(5R) ** (C)** 18/(5R) ** (D)** 4/R ** [JEE’ 2000 (Scr)]**

**(b)** The electron in a hydrogen atom makes a transition from an excited state to the ground state. Which of the following statements 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 total energies decrease and its potential energy increases.

**(D)** Its kinetic, potential and total energies decrease. ** [JEE’ 2000 (Scr)]**

**Q.36 **A hydrogen like atom (described by the Bohr model) is observed to emit six wavelengths, originating from all possible transition between a group of levels. These levels have energies between – 0.85 eV and – 0.544 eV (including both these values)

(a) Find the atomic number of the atom.

(b) Calculate the smallest wavelength emitted in these transitions. ** [JEE’ 2002]**

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**Q.37** In a photoelctric experiment set up, photons of energy 5 eV falls on the cathode having work function 3 eV. (a) If the saturation current is i_{A} = 4μA for intensity 10^{–5} W/m^{2} , then plot a graph between anode potential and current. (b) Also draw a graph for intensity of incident radiation of 2 × 10^{–5} W/m^{2} ? ** [JEE’ 2003]**

**Q.38.** Which of the following statement(s) is (are) correct ?

**(A)** The rest mass of a stable nucleus is less than the sum of the rest masses of its separated nucleons.

**(B)** The rest mass of a stable nucleus is greater than the sum of the rest masses of its separated nucleons.

** (C)** In nuclear fusion, energy is released by fusion two nuclei of medium mass (approximately 100 amu).

** (D)** In nuclear fission, energy is released by fragmentation of a very heavy nucleus ** [JEE’94]**

**Q.39** At a given instant there are 25% undecayed radio- active nuclei in a sample. After 10 sec the number of undecayed nuclei remains to 12.5 % . Calculate :

(i) mean – life of the nuclei and

(ii) The time in which the number of undecayed nuclear will further reduce to 6.25 % of the reduced number ** [JEE 96]**

**Q40**.** (a)** Binding energy per nucleon vs.

** (A)** Y **—>** 2Z **(B)** W **—>** X + Z **(C)** W **—>** 2Y ** (D)** X **—>** Y + Z

**(b)** Order of magnitude of density of Uranium nucleus is, [mP = 1.67 × 1027 kg]

**(A)** 10^{20} kg/m^{3} ** (B)** 10^{17}kg/m^{3} **(C)** 10^{14}kg/m3 ** (D)** 10^{11}kg/m^{3}

**(c)** 22Ne nucleus, after absorbing energy, decays into two α- particles and an unknown nucleus. The unknown nucleus is **(A)** nitrogen** (B)** carbon** (C)** boron **(D)** oxygen

**(d)** Which of the following is a correct statement?

**(A)** Beta rays are same as cathode rays **(B)** Gamma rays are high energy neutrons. **(C)** Alpha particles are singly ionized helium atoms **(D)** Protons and neutrons have exactly the same mass **(E)** None

**(e)** The half – life period of a radioactive element X is same as the mean- life time of another radioactive element Y. Initially both of them have the same number of atoms. Then

**(A)** X & Y have the same decay rate initially **(B)** X & Y decay at the same rate always **(C)** Y will decay at a faster rate than X **(D)** X will decay at a faster rate than Y ** [JEE ’99]**

QUESTIONS |
ANSWERS |

Q1. | 885 |

Q.2 | (a) 2.25eV, (b) 4.2eV, (c) 2.0 eV, 0.5 eV |

Q.3 | (a) 0.6 volt, (b) 2.0 mA |

Q.4 | when the potential is steady, photo electric emission just stop when hυ = (3 + 1)eV = 4.0 eV |

Q.5 | 5.76 × 10^{–11} A |

Q.6 | 15/8 V |

Q.7 | 487.06 nm |

Q.8 | 4.26 m/s, 13.2 eV |

Q.9 | 7 : 36 |

Q.10 | 22.8 nm |

Q.11 | λ_{1}λ_{2 }/ λ_{1} + λ_{2} |

Q.12 | 18/(5R) |

Q.13 | 1.257 × 10^{–23} Am^{2} |

Q.14 | 2.48 ×10^{–12} m |

Q.15 | 5 / 16 , 10^{20} |

Q.16 | 2 eV, 6.53 x 10^{-34} |

Q.17 | 5 |

Q.18 | (i) 5, 16.5 eV, 36.4 A, 340 eV, – 680 eV, h/ 2π 1.06 × 10^{–11} m |

Q.19 | z = 3, n = 7 |

Q.20 | 54.4 eV |

Q.21 | n = 3, 3 : 1 |

Q.22 | 23.6 MeV |

Q.23 | (i) 1.33 × 10^{16} photons/m^{2} – s ; 0.096 μÅ (ii) 2.956 × 10^{15} photons/m2 s ; 0.0213 μA (iii) 1.06 volt |

Q.24 | (i) 2 ; (ii) 23.04 ×10^{–19}J ; (iii) 4 –> 1 , 4 –> 3 |

Q.25 | (i) 1.875 × 10^{4} V, (ii) 2.7 × 10^{–15} J, (iii) 0.737 Å, (iv) 2.67 × 10^{–15} J |

Q.26 | 3.3 × 10^{-6} g |

Q.27 | 1.7 × 10^{10} years |

Q.28 | 5196 yrs |

Q.29 | ΔT = 0.2E_{0} [ αt – α/π (1 – e^{-λt}) ] / mS |

Q.30 | n = 6, Z = 3 |

Q.31 | 10^{5} s^{–1} ; (b) 286.18 ; (d) 111 s |

Q.32 | (i) he / 4πm (ii)ehB / 8πm |

Q.33 | 0.61 Å |

Q.34 | during combination = 3.365 eV; after combination = 3.88 eV (5 –> 3) & 2.63 eV (4 –> 3) |

Q.35 | (a) C, (b) A |

Q.36 | 17 3, 4052.3 nm |

Q.37 | |

Q.38 | A , D |

Q.39 | (i) t _{1/2} = 10 sec. , t_{means} = 14.43 s (ii) 40 seconds |

Q.40 | (a) C ; (b) B ; (c) B ; (d) E ; (e) C |

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