Write the properties of cathode rays.

Give the results of Rutherford alpha scattering experiment.

Write down the postulates of Bohr atom model.

(a) A hydrogen atom is excited by radiation of wavelength 97.5 nm. Find the principal quantum number of the excited state
(b) Show that the total number of lines in emission spectrum is \(\frac { n(n-1) }{ 2 } \) Compute the total number of possible lines in emission spectrum as given in(a).

Calculate the radius of the earth if the density of the earth is equal to the density of the nucleus.[mass of earth 5.97 x 10²⁴ kg].

Calculate the mass defect and the binding energy per nucleon of the \(_{ 47 }^{ 108 }{ Ag }\) nucleus. [atomic mass of Ag = 107.905949]

Half lives of two radioactive elements A and B are 20 minutes and 40 minutes respectively. Initially, the samples have equal number of nuclei. Calculate the ratio of decayed numbers of A and B nuclei after 80 minutes.

On your birthday, you measure the activity of the sample ²¹⁰Bi which has a half-life of 5.01 days. The initial activity that you measure is 1µCi.
(a) What is the approximate activity of the sample on your next birthday? Calculate
(b) the decay constant
(c) the mean life
(d) initial number of atoms.

Calculate the time required for 60% of a sample of radon undergo decay. Given T_1/2 of radon = 3.8 days.

Find the (i) angular momentum (ii) velocity of the electron revolving in the 5^th orbit of hydrogen atom.
(h = 6.6 x 10^–34 Js, m = 9.1 x 10^–31 kg)

(a) Show that the ratio of velocity of an electron in the first Bohr orbit to the speed of light c is a dimensionless number.
(b) Compute the velocity of electrons in ground state, first excited state and second excited state in Bohr atom model for hydrogen atom.

The Bohr atom model is derived with the assumption that the nucleus of the atom is stationary and only electrons revolve around the nucleus. Suppose the nucleus is also in motion, then calculate the energy of this new system.

Suppose the energy of an electron in hydrogen–like atom is given as E_n = \(-\frac { 54.4 }{ { n }^{ 2 } } eV\) where \(n \in \mathbb{N}\) . Calculate the following:
(a) Sketch the energy levels for this atom and compute its atomic number.
(b) If the atom is in ground state, compute its first excitation potential and also its ionization potential.
(c) When a photon with energy 42 eV and another photon with energy 51 eV are made to collide with this atom, does this atom absorb these photons?
(d) Determine the radius of its first Bohr orbit.
(e) Calculate the kinetic and potential energies of electron in the ground state.

(a) Calculate the disintegration energy when stationary \(_{ 92 }^{ 232 }{ U }\)  nucleus decays to thorium \(_{ 90 }^{ 228 }{ Th }\)  with the emission of α particle. The atomic masses are of  \(_{ 92 }^{ 232 }{ U }\) = 232.037156 u, \(_{ 90 }^{ 228 }{ Th }\) = 228.028741u and \(_{ 2 }^{ 4 }{ He }\) = 4.002603 u
(b) Calculate kinetic energies of \(_{ 90 }^{ 228 }{ Th }\) and α-particle and their ratio.

A radioactive sample has 2.6μg of pure \(_{ 7 }^{ 13 }{ N }\) which has a half-life of 10 minutes.
(a) How many nuclei are present initially?
(b) What is the activity initially?
(c) What is the activity after 2 hours? (d) Calculate mean life of this sample.

Keezhadi ((கீழடி),a small hamlet, has become one of the very important archaeological places of Tamilnadu. It is located in Sivagangai district. A lot of artefacts (gold coins, pottery, beads, iron tools, jewellery and charcoal, etc.) have been unearthed in Keezhadi which have given substantial evidence that an ancient urban civilization had thrived on the banks of river Vaigai. To determine the age of those materials, the charcoal of 200 g sent for carbon dating is given in the following figure (b). The activity of \(_{ 6 }^{ 14 }{ C }\) is found to be 37 decays/s. Calculate the age of charcoal.

Figure (a) Keezhadi – excavation site

Figure (b) – Characol which was sent for carbon dating