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

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#### Chapters ## Chapter 15: Structure of Atoms and Nuclei

Exercises
Exercises [Pages 342 - 343]

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

Exercises | Q 1.1 | Page 342

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

Exercises | Q 1.2 | Page 342

Choose the correct option.

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

• 2

• 4

• 8

• 16

Exercises | Q 1.3 | Page 342

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

Exercises | Q 1.4 | Page 342

Choose the correct option.

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

• Radius

• Mass

• Volume

• Density

Exercises | Q 1.5 | Page 342

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

Exercises | Q 2.1 | Page 342

Answer in brief.

State the postulates of Bohr’s atomic model.

Exercises | Q 2.2 | Page 342

Answer in brief.

State the difficulties faced by Rutherford’s atomic model.

Exercises | Q 2.3 | Page 342

Answer in brief.

What are alpha, beta and gamma decays?

Exercises | Q 2.4 | Page 342

Define excitation energy.

Exercises | Q 2.4 | Page 343

Define binding energy.

Exercises | Q 2.4 | Page 342

Define ionization energy of an electron in an atom.

Exercises | Q 2.5 | Page 342

Answer in brief.

Show that the frequency of the first line in the Lyman series is equal to the difference between the limiting frequencies of Lyman and the Balmer series.
Exercises | Q 3 | Page 342

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

Exercises | Q 4 | Page 342

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.

Exercises | Q 5 | Page 342

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

Exercises | Q 6 | Page 342

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

Exercises | Q 7 | Page 342

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

Exercises | Q 8 | Page 342

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

Exercises | Q 9.1 | Page 342

Describe the principles of a nuclear reactor.

Exercises | Q 9.2 | Page 342

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

Exercises | Q 10 | Page 342

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

Exercises | Q 11 | Page 342

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?

Exercises | Q 12 | Page 342

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.

Exercises | Q 13 | Page 342

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.

Exercises | Q 14.1 | Page 343

Complete the following equation describing nuclear decay.

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

Exercises | Q 14.2 | Page 343

Complete the following equation describing nuclear decay.

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

Exercises | Q 14.3 | Page 343

Complete the following equation describing nuclear decay.

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

Exercises | Q 14.4 | Page 343

Complete the following equation describing nuclear decay.

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

Exercises | Q 15.1 | Page 343

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.

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

Exercises | Q 15.2 | Page 343

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.

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

Exercises | Q 15.3 | Page 343

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.

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

Exercises | Q 16 | Page 343

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 × 10−12per second.

Exercises | Q 17 | Page 343

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

Exercises | Q 18 | Page 343

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?

Exercises | Q 19 | Page 343

Disintegration rate of a sample is 1010 per hour at 20 hours from the start. It reduces to 6.3 x 109 per hour after 30 hours. Calculate its half-life and the initial number of radioactive atoms in the sample.

Exercises | Q 20 | Page 343

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

c) What will be the activity after one year?

Exercises | Q 21 | Page 343

A source contains two species of phosphorous nuclei, $\ce{_15^32P}$ (T1/2 = 14.3 d) and $\ce{_15^33P}$ (T1/2 = 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 $\ce{_15^32P}$?

Exercises | Q 22 | Page 343

Before the year 1900 the activity per unit mass of atmospheric carbon due to the presence of 14C averaged about 0.255 Bq per gram of carbon.
(a) What fraction of carbon atoms were 14C?
(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 14C is 5730 years.

Exercises | Q 23 | Page 343

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

Exercises | Q 24 | Page 343

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.

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## Chapter 15: Structure of Atoms and Nuclei

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

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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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