(a) Define the term decay constant and half life of a radioactive sample. Derive the relation connecting the two.

(b) How many disintegrations per second will occur in one gram of ₉₂U²³⁸, if its half-life against alpha decay is \(1.42\times { 10 }^{ 17 }s\) ?

3

(a)

A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n=4 level.Determine the wavelength and frequency of photon.

3

(a)

(a)Using the Bohr's model, calculate the speed of the electron in a hydrogen atom in the n=1,2, and 3 levels (b)Calculate orbital period in each of these levels.

3

(a)

Obtain the first Bohr radius and the ground state energy of a 'muonic hydrogen atom'(i.e. an atom in which a negatively charged moun (\(\mu^-\)) of mass about 207 m_e orbits around a proton.

3

(a)

What is the minimum energy that must b given to a H-atom in ground state so that it can angular momentum of the system is conserved, what would be the angular momentum of such H photon?

3

(a)

What is Bohr's quantum condition?

3

(a)

The wavelength of \({ K }_{ \alpha }\) line for copper is \(1.36\mathring { A } \) . Calculate the ionisation potential of a K shell electron in copper.

3

(a)

Calculate shortest wavelength of Balmer series.Given \(R=1.097\times { 10 }^{ 7 }{ m }^{ -1 }\).

3

(a)

Calculate the equivalent energy of electron and proton at rest.Given that mass of electron \(=9.1\times { 10 }^{ -31 }kg\) and mass of proton \(=1.673\times { 10 }^{ -27 }kg\quad \) .

3

(a)

The half-life of a certain radioactive material is 100 days. After how much time the undecayed fraction of a material will be 6.25%?

3

(a)

One milligram of thorium emits 22 \(\alpha -particles\) per minute per unit solid angle. Calculate average life of thorium. The Atomic weight of thorium is 232.

3

(a)

A radioactive sample contains 2.2 mg of pure \(_{ 6 }{ { C }^{ 11 } }\) which has half-life of 1224 s. Calculate (i) the number of atoms presents initially (ii) the activity when \(5\mu g\) of the sample will be left?

3

(a)

Assuming that four hydrogen atoms combine to form a helium atom and two positrons, each of mass 0.000549 u, calculate the energy released. Given \(m(_{ 1 }{ { H }^{ 1 }) }\)=1.007825 u and \(m(_{ 2 }{ { He }^{ 4 }) }\)=4.002604 u.

3

(a)

There is a stream of neutrons with a kinetic energy of 0.0327 eV. If the half life of neutrons is 700 seconds, what fraction of neutrons will decay before they travel a distance of 10 m? Given mass of neutron \(=1.675\times { 10 }^{ -27 }kg.\)

3

(a)

Suppose you are given a chance to repeat the alpha particle scattering experiment using a thin sheet of solid hydrogen in place of gold foil. What results do you expect?

3

(a)