# ch18 Flashcards

Rutherford experiment disproved which model for the atom?

describe the model

The Thompson model or plum pudding model

atoms were a plum pudding with electrons embedded throughout a positive sphere

how do you investigate the structure of an atom

with scattering experiments

particles are accelerated to a high energy and directed at a target

Describe Rutherford’s experiment and his results

A stream of alpha particles from a radioactive source was fired at a very thin gold foil.

The angles at which the particles were scattered were recorded

some passed straight through (so most atom is empty space)

but a few of the alpha particles bounced right back from the foil being scattered at angles greater than 90 degrees

What could Rutherford conclude after his experiment?

The atom is mainly empty space.

the core must be massive on an atomic scale to deflect alpha particles through large angles, but its much smaller than an atom as very few particles deflected through more than 90 degrees

alpha particles deflected due to electric repulsion between positively charged alpha particles and positive core in gold atoms.

The centre of the atom must have a large, positive charge. Rutherford named this the nucleus.

The nucleus must be tiny, but massive (mass).

1 in how many alpha particles were turned back and what does this suggest about the size of a nucleus

diameter of atom

diameter of nucleus

1 in 10000 turned around so nucleus is 10 times smaller than the atom

diameter of atom is 10^{-10}m

diameter of nucleus therefore is 10^{-14 }m

what happens to the deflection angle if the alpha particles are slowed done

how is scattering affected if the nuclei has less electric charge

relationship between scatter angle and inverse square law

if alpha particles are slowed down more would be deflected at greater angles since the nucleus would be able to turn them back more easily

nuclei of smaller electric charge scatter alpha particles less strongly

the pattern of number of alpha particles scattered at different angles fits the pattern expected from the inverse square law for electric repulsion

alpha particles are highly ionising and so will lose their energy over a short distance ionising air particles

by evacuating the apparatus (removing air particles) you cen minimise collisions and therefore get an accurate measure of the deflection angles

kinetic energy of alpha particle at its closest approach

0 kinetic energy

what is electrical potential energy equal to at a large distance from the nucleus

at a large distance from the nucleus, alpha particle electrical potential energy is equal to its initial kinetic energy

equation for initial kinetic energy

charge on alpha particle

charge on gold particle

initial kinetic energy = electrical potential energy = kQq / r

alpha: 2e = 2 *(1.6*10^{-19})

gold: 79e = 79 * (1.6*10^{-19})

force that a particle experiences near a nucleus

F = KQq / r²

What did Rutherford discover about charge at the centre of the atom?

Some of the alpha particles were deflected through large angles, so the centre of the atom must have a large positive charge to repel them.

What value do you need when you are estimating the distance of closest approach of an alpha particle that has been fired at a gold nucleus?

The alpha particles initial kinetic energy

What value do you need to find the charge of the nucleus?

The atom‘s proton number, Z

how are electrons similar to alpha particles

electrons are scattered by the nucleus in the same way alpha particles are, but the force is attractive this time.

how to produce high energy electrons

using particle accelerators

one application of particle accelerators

dental x-ray tubes are particle accelerators

electrons boiled off heated wire and accelerated towards positive target

describe the change in energy for electrons in dental x-ray tubes

rearrange to give velocity

electrons lose electrical potential energy (qV) and gain kinetic energy (1/2mv²)

qV = 1/2mv²

can rearrange for v (velocity)

V = accel voltage

q = charge

m = mass of electron

limitations of momentum equation

accurate at low speeds but not at high speeds

when v << c

einstein momentum equation

momentum = relativistic factor * mass * velocity

total energy of free particle

kinetic energy + rest energy

= relativistic factor * m * c²

equation for energy when particle at rest

relativistic factor is 1 at rest so

Erest = mc²

what is rest energy equivalent to

mass

Erest = m

equation to calc relativistic factor using energy

rel factor = Etotal / Erest

ymc² / mc²

what is a linear accelerator and how does it work

a long straight tube containing electrodes which change charge signs

electrons are acclerated between a pair of electrodes which have an alternating current applied to them

its timed so that the electron is always attracted to the next electrode and repelled from the previous one

length of electrodes increases because electrons are getting faster so they must stay in the tube for the same amount of time so that electrodes pd doesn’t change too early

the max speed of the electrons is only limited by the length of the accelerator, so they can approach the speed of light

momentum approximation equation

wavelength equation using this

when v is similar to c we can say momentum = y * m * v goes to momentum = y * m * c

Etotal = y * m * c²

so

p = Etotal / c

λ = h / p

λ = h * c / Etotal

sin theta equation involving nuclear diameter

sin theta = 1.22(wavelength) / nuclear diameter

can get wavelength from hc / E