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

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

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

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

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

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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?

Answer in brief.

State the postulates of Bohr’s atomic model.

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State the difficulties faced by Rutherford’s atomic model.

What is gamma decay?

What is alpha decay?

What is beta decay?

Define the Excitation energy of an electron in an atom.

Define the Binding energy of an electron in an atom.

Define ionization energy of an electron in an atom.

Answer in brief.

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State the postulates of Bohr’s atomic model.

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 is nuclear fission and giving an example. Write down the formula for energy generated in these processes.

Explain what is nuclear fusion and give an example. Write down the formulae for energy generated in 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 americium 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 × 10⁻¹²per 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 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.

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?

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 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.

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.

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.