Explain the closest approach method
The repulsive force between the nucleus and alpha particle reduces the speed of the particle to 0 momentarily.
At this point KE = EPE
The radius can be found equating the two equations
State an advantage of the closest approach method
- Gives a good estimate of the upper limit for a nuclear radius
- Mathematics are very simple
- Particles are scattered only by the protons and not all the nucleons
State 2 disadvantages of the closest approach method
- Value will always be an overestimate
- Alpha particles are hadrons and therefore experience the strong nuclear force which is not accounted for
- Gold nucleus will recoil as alpha particles approaches
- Alpha particles have finite size whereas electrons can be treated as point masses
- Difficult to obtain alpha particles that rebound at 180 degrees
- Alpha particles must all have same initial kinetic energy
- Sample must be extremely thin to prevent multiple scattering
State the equation for electron diffraction
sin ø = 0.61 x de Broglie’s wavelength / R
Why must the de Broglie’s wavelength of an electron be 1fm?
Because the radius of any nucleus is around 1fm, therefore for significant diffraction the wavelength must be similar to the size of the gap
State the equation for nuclear radius
R = k x A^1/3
A - nucleon number
R - nuclear radius
Show that nuclear density is constant for all nuclei
p = mass / volume
P = A x m(nucleon) / 4/3πR^3
P = A x m / 4/3πk^3A
P = m / 4/3πk^3 (constant)
State the equation for De Broglie’s wavelength
h / mv
Explain the electron diffraction method
Electrons are fired at a thin sheet of foil, forming a diffraction pattern with a bright central spot and dimmer concentric circles around it.
A graph of intensity against diffraction angle can be used to find angle of first minimum
Use sinø= 0.61 x DBW / R
State an advantage of the electron diffraction method
- More accurate than closest approach method
- Gives direct measurement of the radius of a nucleus
- Electrons do not interact with nucleons in the nucleus via SNF
State a disadvantage of the electron diffraction approach
- Electrons must be accelerated to very high speeds to minimise DBW and increase resolution
- Electrons can be scattered by nucleons
Can make first minimum difficult to determine
