26.1 - discovery of nucleus

what was the accepted atomic theory before rutherford’s?

thomson’s plum pudding model - that the atom was composed of negatively charged electrons floating in a ‘sea’ of positive matter with no concentration of mass

what was the order of discovery for subatomic particles?

1. electron

2. proton

3. neutron

what is rutherford’s atomic model?

• mass concentrated in the center, in the nucleus

• nucleus composed of protons and neutrons

• positive charge concentrated in the center, in the nucleus

• negatively charged electrons orbiting the nucleus in shells

• strong nuclear force holding the nucleus together, overcoming the electrostatic repulsion of the protons

• atom is majority empty space

• nucleus is roughly 1/10,000 of the size of the atom

thomson vs rutherford

PICTURE TABLE

thomson vs rutherford similarities vs differences

PICTURE TABLE

what did rutherford know about radiation?

1. of it’s existence

2. why particles radiated

3. the 3 kinds of radiation

what was the set up for the gold leaf / rutherford’s scattering experiment?

PICTURE

MUST INCLUDE

• wall / detectors goes all around the apparatus, at a constant distance from the point of impact between beam and metal foil

• alpha particles come from an alpha source

• the metal container is evacuated

• it is a ‘thin gold sheet / foil / leaf’

what happened in rutherford’s scattering experiment?

1. alpha particles, of the same Ek, fired at a thin gold leaf foil

2. majority went straight through

3. 1/2000 particles deflected, 1/10,000 deflected at an angle >90°

4. number of alpha particles reaching the detectors per minute for different angles of reflection are record

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what did rutherford’s scattering experiment prove?

1. the atom was made up of mostly empty space, and that mass was concentrated in the centre, as the majority of alpha particles fired straight through without deflection

2. that the nucleus was roughly 1/10,000 of the size of the atom as 1/10,000 alpha particles would deflect at an angle >90°

3. the nucleus was positively charged because the alpha particles that were deflected at an angle >90° must’ve gone under electrostatic repulsion to be deflected in such a way

4. the existence of the nucleus, for the reasons previously mentioned

5. that the existing atomic theory (thomson’s plum pudding) could be disproved

which particle was used in the gold leaf experiment?

alpha particles (helium nucleus)

in rutherford’s scattering experiment, why was gold used?

it was the only material that could be rolled thin without cracking

in rutherford’s scattering experiment, why did the gold foil have to be thin?

the reduce the layers of atoms as much as possible as that would increase the chance of an alpha particle hitting the nucleus, since the chances of that are 1/10,000n (n = number of layers of atoms)

what are some features of the alpha particles used in rutherford’s scattering experiment?

1. alpha source had a long half-life

2. all alpha particles were fired with the same kinetic energy

3. they were shot in a narrow beam

in rutherford’s scattering experiment, why was it important that all alpha particles were shot with the same Ek?

because slow particle would deflect more than fast particles and that would interfere with the results

in rutherford’s scattering experiment, what does it mean for the metal container to be ‘evacuated’ and why was this important?

• evacuated means there was no air inside

• to prevent air absorbing the alpha particles before they reached the gold foil; prevent deflection ionisation

deflection due to electrostatic forces diagram;

IMAGE

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in rutherford’s scattering experiment, why is it important that the wall / detectors can rotate completely around the apparatus?

so it can detect the deflected alpha particles in whatever direction they are scattered

in rutherford’s scattering experiment, why was it important that the alpha source had a long half-life?

otherwise later readings would be lower than earlier readings due to radioactive decay of the source nuclei

in rutherford’s scattering experiment, why was it important that alpha particles were fired in a narrow beam?

to increase precision and reduce the likelihood of multiple scattering events - which would make it harder to observe the scattering (i.e., the precise angle of deflection) of an individual alpha particle, which was needed to deduce the structure of the atom

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how many alpha particles are deflected?

1/2000

how many alpha particles are deflected at angle >90°?

1/10,000

what causes 180° deflection?

‘head-on’ collision of the alpha particle with the nucleus

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what is the diameter of a nucleus measured in?

femtometres (fm), x10¹⁵ m

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what causes greater deflection?

1. increased electrostatic repulsion of the alpha particle and the neutron

2. decreased separation (i.e., closer proximity) of the alpha particle and the nucleus

smaller least distance of approach (closer they are) = greater the electrostatic force of repulsion = more deflection

what is the least distance of approach?

the closest an alpha particle can get to a positively charged nucleus before the electrostatic force of repulsion deflects the alpha particle back

what happens the closer the alpha particle is to ‘head-on’ collision?

1. the greater the deflection - since electrostatic repulsion (therefore deflection) increases with decreased separation

2. the smaller the least distance of approach

DIAGRAM

what is the magnitude of charge of a nucleus?

+Ze

+ = nucleus has a positive charge

Z = atomic number of element (number of protons)

e = electron charge (protons and electrons have the same charge)

where does the equation for magnitude of charge of an electron come from?

using coulomb’s law of force and neutron’s laws of motion

FURTHER RESEARCH NEEDED

what is the symbol for ‘number of layers of atoms’?

n

what is the probability that an alpha particle hits the nucleus?

1/10,000n

n is the layers of atoms

DIAGRAM

what does the probability that an alpha particle hits the nucleus depend on?

the effective area of the cross-section of the nucleus as compared to that atom

CLARIFY

what is the area ratio for a nucleus of diameter (d) in an atom of diameter (D)?

¼πd² / ¼πD² (area of nucleus / area of atom),

rearranged into d² = D² / 10,000n

LOOK INTO DERIVATION

when is the alpha particle at the least distance of approach to the nucleus?

in a head-on collision

what is the kinetic energy of an alpha particle in head-on collisions?

• in the least distance of approach, the Ek of the alpha = the Ep of the alpha in the nucleus’ electric field

• Ek = (QαQ𝑛) / (4πε₀d)

Qα = alpha charge

Q𝑛 = nucleus charge (+Ze)

ε₀ = vacuum permittivity of free space, 8.85 × 10^–12 F m^–1

d = distance of approach

what is (vacuum) permittivity of free space (ε₀)?

• a measure of how easy it is to generate an electric field in a certain material

• a constant

• 8.85 × 10^–12 F m^–1