The electron in the hydrogen atom passes from the n = 4 energy level to the n = 1  level.What is the maximum number of photons that can be emitted? and minimum number?

2

(a)

If elements with principal quantum number n > 4 did not exist in nature, what would be the possible number of elements?

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(a)

How many electrons, protons, and neutrons are there in a nucleus of atomic number 11 and mass number 24?

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(a)

Give the order of magnitude of nuclear mass density and average atomic mass density. Compare these densities with the typical mass density of solids, liquids, and gases (at ordinary temperature and pressure).

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(a)

Why is \(_{ 92 }{ { U }^{ 238 } }\) not suitable for chain reaction?

2

(a)

Why is neutron so effective as a bombarding particle?

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Are the nucleons fundamental particles, or do they consist of still smaller parts? One way to find out is to probe a nucleon just as Rutherford probed an atom. What should be the kinetic energy of an electron for it to be able to probe a nucleon? Assume the diameter of a nucleon to be approximately \({ 10 }^{ -15 }m.\)

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The radius of the innermost electron orbit of a H-atom is 5.3 x 10^-11 m. What are the radii of the n = 2 and n = 3 orbits?

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Show that the density of nucleus over a wide range of nuclei is constant independent of mass number.

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Derive the expression for the law of radioactive decay of a given sample having initially No decaying to the number N present at any subsequent time t.
Plot a graph showing the variation of the number of nuclei versus the time lapsed. Mark a point on the plot in terms of T_1/2 value the number present N = No / 16.

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(a)

Calculate the de-Broglie wavelength of the electron orbiting in the n = 2 states of hydrogen atom

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Show that the radius of the orbit in hydrogen atom varies as n², where n is the principal quantum number of the atom.

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Write nuclear equations for
a) The \(\alpha\)-decay of ²²⁶Ra₈₈
b) The \(\beta\)^- -decay of ³²P₁₅
c) The \(\beta\)⁺ decay of ³²P₁₅

2

(a)

A neutron is absorbed by a ⁶Li3 nucleus with the subsequent emission of an alpha particle.
i) Write the corresponding nuclear reactions.
ii) Calculate the energy released in MeV, in this reaction.
Given mass ⁶Li3 = 6.0151264; mass (neutron) = 1.00966544
Mass (alpha particle) = 4.00260444 and mass(triton) = 3.01000004

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(a)