CBSE Class 12 Physics Modern Physics Basic Problems

CBSE Class 12 Physics Modern Physics Basic Problems. Please refer to the examination notes which you can use for preparing and revising for exams. These notes will help you to revise the concepts quickly and get good marks.'

Structure of Atoms - Structure of An Atom

An Atomic Number is the number of protons in an atom.
The arrangement of electrons in various energy levels of an atom known as electronic configuration
The maximum number of electrons in any energy level of the atom is given by 2n².
The outcome shell of an atom cannot accommodate more than eight electrons.
Combining capacity of the atoms to form molecules either with the same or different elements is known as valency.
Neutron is a neutral particle present in the nucleus.
The total number of protons and neutrons present in one atom of an element is referred as atomic mass.
Isotopes are atoms with same atomic number but different mass number.
Isotopes of certain elements are used in a nuclear reactor, and in the treatment of cancer and goitre.
Atoms of different elements with different atomic number that have the same mass number are called Isobars.

Isotopes and Isobars

Mass number is the sum of the number of protons and the number of neutrons.
The atomic number is the number of protons.
Isotopes have same number of protons but different number of neutrons.
As the Isotopes have the same number of electrons and protons, they have similar chemical properties.
Isobars are the atoms of different elements having different atomic numbers but same mass numbers.
Isobars have different chemical properties because they have different atomic numbers but same mass numbers.

Nuclear Binding Energy and Nuclear Stability

Mass defect (m) is the different between the theoretically expected mass of the nucleus and the actual mass of the nucleus.
The energy equivalent to the mass defect is called the binding energy (Eb). This energy is released when the constituents of a nucleus are brought together. This same energy is required to break a nucleus into its constituent nucleons.
The ratio of the binding energy to mass number of nucleus is called as the binding energy per nucleon or average binding energy (Ebn).
Nuclear force is a strong attractive force between the nucleons in the nucleus, which binds the nucleons together in the tiny nuclear volume in spite of the coulomb repulsive forces that exist between the positively charged protons.
Nuclear force is short ranged but is the strongest force in nature.
Nuclear forces are independent of charge.
A nucleon will be under the influence of some of its neighbours, which come within the range of the nuclear force.
The property that a given nucleon is influenced only by nucleons close to it is referred to as the saturation property of the nuclear force.

Alpha, Beta, and Gamma Decay

During a radioactive decay process, the original nucleus is referred as parent nucleus and the residual or resultant nucleus is referred as daughter nucleus.
In nature, a radioactive nucleus can decay by three modes namely alpha decay, beta decay and gamma decay.
In alpha decay, a radioactive nucleus emits a helium nucleus, which is referred to as an alpha particle.
The difference between the rest mass energy of the final products is called the Q value of the reaction.
In beta-minus decay, a neutron transforms into a proton within the nucleus.
Along with this transformation, an electron and an antineutrino are also emitted.
In beta- plus decay, the radioactive nucleus emits a high- energy photon.

Nuclear Energy

When tightly bound nuclei transform into relatively less tightly bound nuclei, nuclear energy is released.
The nuclear energy obtained for the same mass is enormous compared to that of the conventional sources of energy.
When neutrons are bombarded onto various elements, new radioactive elements can be produced.
A nuclear fission process generates an enormous amount of heat energy.
Nuclear fission products are highly rich in neutrons, and are unstable and radioactive. They emit beta particles in succession until they reach a stable endproduct.

Nuclear Fission

When the nucleus of a heavy element is bombarded with neutrons splits into two or more smaller nuclei and releases energy. Such a process is called “nuclear fission”.
The amount of energy released in each fission reaction is 200 MeV.
A nuclear chain reaction is a process in which a series of self-sustained nuclear fissions take place as the neutrons produced in each fission cause additional fissions.
Reproduction factor k is defined as the ration of the number of neutrons present in a particular generation to the number of neutrons present in the preceding generation.
The nuclear waste produced in a nuclear reactor is extremely hazardous and must be handled carefully.

Nuclear Fusion

The nuclear reaction in which lighter nuclei combine to form a heavier nucleus with the release of an enormous amount of energy is called “nuclear fusion”.
The energy released per nucleon is much higher in a nuclear fusion reaction than in a nuclear fission reaction.
Nuclear fusion reactions can take place only at very high temperatures.
Nuclear fusion reactions that take place at very high temperatures are called “thermo-nuclear reactions”.

1. A single electron moves in the orbit of a stationary nucleus of charge +Ze. It requires 16.53 eV to excite the electron from third orbit to fourth orbit. Find
(a) the value of Z,
(b) the energy required to excite the electron from the fourth orbit to fifth orbit,
(c) the wavelength of electromagnetic radiation to remove the electron from first orbit to infinity and
(d) the radius of first Bohr orbit.

2. The wavelength of the first orbit of Lyman series for hydrogen is equal to that of the second line of Balmer series for some hydrogen like ion. Find the atomic number of ion and energy difference between first and fourth level.

3. An electric lamp is rated at 150 watts in which light energy is emitted with a mean wavelength of 4500Å at an efficiency of 8%. Find the number of photons emitted by the lamp per second.

4. Find the wavelength of Kα X-rays emitted by an element having Z = 79. Given that Moseley’s constants are a = 2.468 × 1015 s^–1 and b = 1.

5. In an experiment, tungsten cathode is irradiated by ultraviolet light of wavelength 1800 Å. If the threshold wavelength for tungsten is 2300 Å, find
(a) the maximum and minimum energy of the emitted photoelectron and
(b) the work function for tungsten.

6. Light from a discharge tube containing hydrogen atom falls on the surface of a piece of sodium of work function 1.82 eV. The kinetic energy of the fastest photoelectron emitted from sodium is 0.73 eV. Find
(a) the energy of photons causing the photoelectric emission,
(b) the quantum number of two levels involved in the emission of these two photons and
(c) the change in the agular momentum of the electron in the hydrogen atom in the above mentioned transition.

7. Two monochromatic beams of light of wavelengths 800 Å and 700 Å are incident on hydrogen atoms in their ground states. These emit electrons with kinetic energies 1.8 eV and 4.0 eV respectively. Find the value of Planck’s constant.

8. A radioactive source is in the form of a metal sphere of diameter 10^–3 m and it emits beta particles at a constant rate of 6.25 × 10¹⁰ particles per second. If the source is electrically insulated, how long will it take for its potential to rise by 1.0 volt, assuming that 80% of the emitted beta particles escape from the
source.

9. A reactor U²³⁵ for producing fission by slow neutrons which release an average energy of 200 MeV per fission. Find the amount of U²³⁵ required for the production of nuclear power at a rate of 32000 kilowatts for 200 hours of operation of this reactor.

10. Find the atomic mass of ₁₇Cl³⁵ nucleus, if its binding energy is 298 MeV. The mass of hydrogen atom and neutron are 1.008143 and 1.008986 units respectively.

11. In a nuclear reaction, fission is produced in 1 gm of U²³⁵ of mass 235.0349 a.m.u. in 24 hours by a slow neutron of mass 1.0087 a.m.u. Assuming that ₃₆Kr⁹² and ₅₆Ba¹⁴¹ of mass 91.8973 a.m.u. and 140.9139 a.m.u. respectively are produced in all reactions, find the total energy produced in kilowatt-hours.

12. Calculate the de Broglie wavelength of an α-particle of mass 6.576 × 10^–27 kg and charge 3.2 × 10^–19 coulomb, accelerated through 2000 V.

13. The wavelength of the yellow line of sodium is 5900 Å. At what kinetic energy would an electron have the same de Broglie wavelenght?

14. The energy of an excited hydrogen atom is –3.4 eV. Calculate the angular momentum of the electronaccording to Bohr’s theory. Given ground state energy of the hydrogen atom as –13.6 eV.

15. Suppose the potential energy between electron and proton at a distance r is given by− ke²/ 3r³. Use Bohr’stheory to obtain energy levels of such a hypothetical atom.

Basic Problems

1. (a) 5 (b) 7.65 eV (c) 36.49 Å (d) 1.06 × 10^–11 m   2. 2, 51.0 eV   3.  2.717 × 10¹⁹    4. 0.1997 Å  5. (a) 1.485 eV, zero, (b) 5.38 eV   6. (a) 2.55 eV (b) 2 and 4 (c) 2.1 × 10^–34   7. 6.57 × 10^–34 J.s.   8. 6.95 μ sec. 9.  15312 gm   10. 34.980094 units    11. 2.28 × 10⁴ Kwh   12. 2.285 × 10^–13 m  13. 4.3 × 10^–6 eV  14. 2.1 × 10^–34 J  s

 15. En =n⁶h⁶/6m³k²e⁴