#### Chapters

Chapter 2: Mechanical Properties of Fluids

Chapter 3: Kinetic Theory of Gases and Radiation

Chapter 4: Thermodynamics

Chapter 5: Oscillations

Chapter 6: Superposition of Waves

Chapter 7: Wave Optics

Chapter 8: Electrostatics

Chapter 9: Current Electricity

Chapter 10: Magnetic Fields due to Electric Current

Chapter 11: Magnetic Materials

Chapter 12: Electromagnetic induction

Chapter 13: AC Circuits

Chapter 14: Dual Nature of Radiation and Matter

Chapter 15: Structure of Atoms and Nuclei

Chapter 16: Semiconductor Devices

## Chapter 15: Structure of Atoms and Nuclei

### Balbharati solutions for Physics 12th Standard HSC Maharashtra State Board Chapter 15 Structure of Atoms and Nuclei Exercises [Pages 342 - 343]

**Choose the correct option.**

In which of the following systems will the radius of the first orbit of the electron be smallest?

hydrogen

singly ionized helium

deuteron

Tritium

**Choose the correct option.**

The radius of the 4^{th} orbit of the electron will be smaller than its 8^{th} orbit by a factor of

2

4

8

16

**Choose the correct option.**

In the spectrum of the hydrogen atom which transition will yield the longest wavelength?

n = 2 to n = 1

n = 5 to n = 4

n = 7 to n = 6

n = 8 to n = 7

**Choose the correct option.**

Which of the following properties of a nucleus does not depend on its mass number?

Radius

Mass

Volume

Density

**Choose the correct option.**

If the number of nuclei in a radioactive sample at a given time is N, what will be the number at the end of two half-lives?

N/2

N/4

3N/4

N/8

**Answer in brief.**

State the postulates of Bohr’s atomic model.

**Answer in brief.**

State the difficulties faced by Rutherford’s atomic model.

**Answer in brief.**

What are alpha, beta and gamma decays?

Define excitation energy.

Define binding energy.

Define ionization energy of an electron in an atom.

**Answer in brief.**

State the postulates of Bohr’s atomic model and derive the expression for the energy of an electron in the atom.

Starting from the formula for the energy of an electron in the nth orbit of the hydrogen atom, derive the formula for the wavelengths of Lyman and Balmer series spectral lines and determine the shortest wavelengths of lines in both these series.

Determine the maximum angular speed of an electron moving in a stable orbit around the nucleus of the hydrogen atom.

Determine the series limit of Balmer, Paschen, and Pfund series, given the limit for Lyman series is 912 Å.

Describe alpha, beta and gamma decays and write down the formulae for the energies generated in each of these decays.

Explain what are nuclear fission and fusion giving an example of each. Write down the formulae for energy generated in each of these processes.

Describe the principles of a nuclear reactor.

What is the difference between a nuclear reactor and a nuclear bomb?

Calculate the binding energy of an alpha particle given its mass to be 4.00151 u.

An electron in hydrogen atom stays in its second orbit for 10^{−8} s. How many revolutions will it make around the nucleus at that time?

Determine the binding energy per nucleon of the amenctum isotope \[\ce{_95^244Am}\], given the mass of \[\ce{_95^244Am}\] to be 244.06428 u.

Calculate the energy released in the nuclear reaction \[\ce{_3^7Li + p ->2\alpha}\] given mass of \[\ce{_3^7Li}\] atom and of helium atom to be 7.016 u and 4.0026 u respectively.

**Complete the following equation describing nuclear decay.**

\[\ce{_88^226Ra->_2^4\alpha{ +}}\] _____

**Complete the following equation describing nuclear decay.**

\[\ce{_8^19O->e^- { +}}\] _____

**Complete the following equation describing nuclear decay.**

\[\ce{_90^228Th->\alpha { +}}\] _____

**Complete the following equation describing nuclear decay.**

\[\ce{_7^12N -> _6^12C {+}}\] ______

Calculate the energy released in the following reaction, given the masses to be

\[\ce{_88^223Ra}\] : 223.0185 u, \[\ce{_82^209Pb}\] : 208.9811 u, \[\ce{_6^14C}\] : 14.00324 u, \[\ce{_92^236U}\] : 236.0456 u, \[\ce{_56^140Ba}\] : 139.9106 u, \[\ce{_92^36Kr}\] : 93.9341 u, \[\ce{_11^6C}\] : 11.01143 u, \[\ce{_11^5B}\] : 11.0093 u. Ignore neutrino energy.

\[\ce{_88^223Ra -> _82^209Pb + _6^14C}\]

Calculate the energy released in the following reaction, given the masses to be

\[\ce{_88^223Ra}\] : 223.0185 u, \[\ce{_82^209Pb}\] : 208.9811 u, \[\ce{_6^14C}\] : 14.00324 u, \[\ce{_92^236U}\] : 236.0456 u, \[\ce{_56^140Ba}\] : 139.9106 u, \[\ce{_36^94Kr}\] : 93.9341 u, \[\ce{_6^11C}\] : 11.01143 u, \[\ce{_5^11B}\] : 11.0093 u. Ignore neutrino energy.

\[\ce{_92^236U -> _56^140Ba + _36^94Kr + 2n}\]

Calculate the energy released in the following reaction, given the masses to be

\[\ce{_88^223Ra}\] : 223.0185 u, \[\ce{_82^209Pb}\] : 208.9811 u, \[\ce{_6^14C}\] : 14.00324 u, \[\ce{_92^236U}\] : 236.0456 u, \[\ce{_56^140Ba}\] : 139.9106 u, \[\ce{_36^94Kr}\] : 93.9341 u, \[\ce{_6^11C}\] : 11.01143 u, \[\ce{_5^11B}\] : 11.0093 u. Ignore neutrino energy.

\[\ce{_6^11C -> _5^11B + e^+ + neutrino}\]

Sample of carbon obtained from any living organism has a decay rate of 15.3 decays per gram per minute. A sample of carbon obtained from very old charcoal shows a disintegration rate of 12.3 disintegrations per gram per minute. Determine the age of the old sample given the decay constant of carbon to be 3.839 × 10^{−12}per second.

The half-life of \[\ce{_38^90Sr}\] is 28 years. Determine the disintegration rate of its 5 mg sample.

What is the amount of \[\ce{_27^60Co}\] necessary to provide a radioactive source of strength 10.0 mCi, its half-life being 5.3 years?

Disintegration rate of a sample is 10^{10} per hour at 20 hours from the start. It reduces to 6.3 x 10^{9} per hour after 30 hours. Calculate its half-life and the initial number of radioactive atoms in the sample.

The isotope \[\ce{^57Co}\] decays by electron capture to \[\ce{^57Fe}\] with a half-life of 272 d. The \[\ce{^57Fe}\] nucleus is produced in an excited state, and it almost instantaneously emits gamma rays.

(a) Find the mean lifetime and decay constant for ^{57}Co.

(b) If the activity of a radiation source ^{57}Co is 2.0 µCi now, how many ^{57}Co nuclei does the source contain?

c) What will be the activity after one year?

A source contains two species of phosphorous nuclei, \[\ce{_15^32P}\] (T_{1/2} = 14.3 d) and \[\ce{_15^33P}\] (T_{1/2} = 25.3 d). At time t = 0, 90% of the decays are from \[\ce{_15^32P}\]. How much time has to elapse for only 15% of the decays to be from \[\ce{_15^32P}\]?

Before the year 1900 the activity per unit mass of atmospheric carbon due to the presence of ^{14}C averaged about 0.255 Bq per gram of carbon.

(a) What fraction of carbon atoms were ^{14}C?

(b) An archaeological specimen containing 500 mg of carbon, shows 174 decays in one hour. What is the age of the specimen, assuming that its activity per unit mass of carbon when the specimen died was equal to the average value of the air? The half-life of ^{14}C is 5730 years.

How much mass of ^{235}U is required to undergo fission each day to provide 3000 MW of thermal power? Average energy per fission is 202.79 MeV.

In a periodic table the average atomic mass of magnesium is given as 24.312 u. The average value is based on their relative natural abundance on earth. The three isotopes and their masses are\[\ce{_12^24Mg}\](23.98504 u), \[\ce{_12^25Mg}\] (24.98584 u), and \[\ce{_12^26Mg}\] (25.98259 u). The natural abundance of \[\ce{_12^24Mg}\] is 78.99% by mass. Calculate the abundances of other two isotopes.

## Chapter 15: Structure of Atoms and Nuclei

## Balbharati solutions for Physics 12th Standard HSC Maharashtra State Board chapter 15 - Structure of Atoms and Nuclei

Balbharati solutions for Physics 12th Standard HSC Maharashtra State Board chapter 15 (Structure of Atoms and Nuclei) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the Maharashtra State Board Physics 12th Standard HSC Maharashtra State Board solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Physics 12th Standard HSC Maharashtra State Board chapter 15 Structure of Atoms and Nuclei are Structure of Atoms and Nuclei, Thomson’S Atomic Model, Geiger-marsden Experiment, Rutherford’S Atomic Model, Atomic Spectra, Bohr’s Atomic Model, Atomic Nucleus, Nuclear Binding Energy, Radioactive Decays, Law of Radioactive Decay, Nuclear Energy.

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