Rutherford's α-Scattering Experiment

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Thomson's Atomic Model:

According to this model, an atom consists of a positively charged sphere in which entire mass & positive charge of the atom is uniformly distributed. Inside this sphere, the electrons are embedded like seeds in a watermelon or like plums in a pudding. The number of electrons is such that their negative charge is equal to positive charge. Thus, atoms is electrically neutral.

Limitations of Thomson's Model:

i. Could not explain the origin of spectral series of hydrogen & other atoms.

ii. Could not explain large angle scattering of α - particles observed by Rutherford.

Rutherford's α-scattering experiment:

An α - particle is He nucleus containing 2 protons & 2 neutrons. It has 4 units of mass & 2 units of positive charge. Many radioactive elements emit α - particles.

S is a radioactive source contained in a lead cavity. The α - particle emitted by the source are collimated into narrow beam with the help of collimator. The collimated beam is allowed to fall on a thin gold fail of thickness ≈ 10^–5 m. α - particles are scattered in different directions are observed though a rotatable detector consisting of ZnS screen & a microscope. The α – particles produce bright flashes on ZnS screen. These are observed by the microscope &counted at different scattering angle θ.

Observations:

i. Most of the α - particle pass straight through the gold foil or suffered very small angle of deflections.

ii. A few a- particles scatter through large ogles ( > 90°).

iii. Rarely, an α - particle rebounces i.e., scattered through an angle of 180°

Explanation:

i. Since most of the α - particles passed undeviated, the atom has a lot of empty space in it.

ii. To explain large scattering of α - particles, Rutherford suggested that all the positive charge & entire mass of the atom is confined to an extremely small central core called as nucleus.

iii. The scattering of α - particles through different angles was explained as :

The α - particles I, I’. Which pass through the atom at a large distance from from the nucleus experience a small electrostatic force of repulsion & undergo a small defection. The α - particles 2. 2’ which pass through the atom at a close distance from the nucleus suffer a larger defection. The α – particle 3, which travels directly towards the nucleus shows down, comes to rest & is deflected through 180° and hence retraces its path.

The graph between scattering angle θ & the number of α - particles directly scatted N is as shown:

Distance of closet Approach:

An α - particle travelling towards the center of the nucleus slows down as it approaches the nucleus. At a certain distance, say r₀ from the nucleus, the α -particle comes to rest for a moment and then retraces it path. It initial kinetic energy is completely converted into electrostatic potential energy. This distance r₀ is called the distance of closest approach. This distance gives an estimate of the size of the nucleus.

Mathematically,

mv² =

where 2e is the charge on α - particle and Ze is the charge on nucleus.

=

Impact Parameter:

Impact parameter is defined as the perpendicular distance of the velocity vector of the α - particle from the center of the nucleus, when it is far away from the nucleus of the atom. Rutherford derived the relation between impact parameter and scattering angle, which is given by

b =