Kompetensi 1:

Mahasiswa mampu menjelaskan konsep kuantisasi energi

Blackbody radiation

Radiasi benda hitam Teori

atom BohrHipotesa

de Broglie

Struktur atom hidrogen

Gerakan partikel dalam kotak

Gerakan vibrasi Geraka

n rotasi

Struktur molekul

Metode pendekatan, metode LCAO, unsur dan operasi simetri

Quantum chemistry

Spektroskopi

Spektrum dalam kimia

J.J ThomsonThe discoverer of the electron

Sir Joseph John Thomson

Sir Joseph John “J.J.” Thomson, (18 December 1856 – 30 August 1940) was a British physicist and Nobel laureate, credited for the discovery of the electron and of isotopes, and the invention of the mass spectrometer. He was awarded the 1906 Nobel Prize in Physics for the discovery of the electron and his work on the conduction of electricity in gases.

Sinar Katoda

Thomson telah melakukan sebuah seri percobaan dengan sinar katoda dan tabung sinar katoda yang akhirnya membuatnya menemukan elektron dan partikel sub atom.

3 Percobaan Thomson:Percobaan pertamaPercobaan keduaPercobaan ketiga

Thomson’s first experiment

In his first experiment, he investigated whether or not the negative charge could be separated from the cathode rays by means of magnetism.

He constructed a cathode ray tube ending in a pair of cylinders with slits in them. These slits were in turn connected to an electrometer. Thomson found that if the rays were magnetically bent such that they could not enter the slit, the electrometer registered little charge.

Thomson concluded that the negative charge was inseparable from the rays.

Thomson’s second experiment

In his second experiment, he investigated whether or not the rays could be deflected by an electric field (something that is characteristic of charged particles). Previous experimenters had failed to observe this, but Thomson believed their experiments were flawed because they contained trace amounts of gas. Thomson constructed a cathode ray tube with a practically perfect vacuum, and coated one end with phosphorescent paint. Thomson found that the rays did indeed bend under the influence of an electric field, in a direction indicating a negative charge.

Thomson’s third experiment

In his third experiment, Thomson measured the mass-to-charge ratio of the cathode rays by measuring how much they were deflected by a magnetic field and how much energy they carried. He found that the mass to charge ratio was over a thousand times lower than that of a hydrogen ion (H+), suggesting either that the particles were very light or very highly charged.Thomson's conclusions were bold: cathode rays were indeed made of particles which he called "corpuscles", and these corpuscles came from within the atoms of the electrodes themselves, meaning that atoms are in fact divisible. The "corpuscles" discovered by Thomson are identified with the electrons which had been proposed by G. Johnstone Stoney.

Blackbody radiation

When a body is heated it emits radiation with a continuous distribution of wavelengths.

The intensity of the radiation depends both on the nature of the surface of the body and on the temperature of the body.

To simplify the discussion concerning the nature of the surface, we often consider an ideal body, a Black Body, which absorbs and emits all wavelengths of electromagnetic radiation.

A good approximation to an ideal black body is a small hole drilled into the side of a closed box.

The radiation emitted by such an ideal body is called Black Body Radiation.

Blackbody radiation

A plot of the intensity of blackbody radiation versus frequency for several temperature

Rayleigh-Janes Law

dvvc

kTdvT 2

3

8),(

(v,T)dv is the density of radiative energy between the frequency v and v+dv and has units of joules/cubic meter (Jm-

3)

K is the Boltzman constant (the ideal gas constant divided by Avogadro’s number

T is the absolute temperature

C is the speed of light

1.1

Spectrum electromagnetic

Depicts white light being separated into different frequency waves.

Spectrum electromagnetic

Plank used a Quantum hypothesis to derive the black body radiation

Plank’s assumption: The radiation emitted by the body was due

to the oscillations of the electrons in the constituent particles of the material body.

The energies of the oscillators had to be proportional to an integral multiple of the frequency or in an equation, that =nhv, where n is an integer, h is a proportionality constant and v is the frequency

Planck’s distribution law

Using statistical thermodynamic arguments, Planks was able to derive the equation:

1

8),(

/3

3

kThve

dv

c

hvdvTv

Planck was able to show that this equation gives excellent agreement with the experimental data for all frequencies and temperatures if h has the value 6.626x10-34 joule seconds (Js)

h is called Planck’s constant and the equation is known as Planck’s distribution law for black body radiation

1.2

Spectrum electromagnetic

Learning by simulation

Planck’s black body radiation law

http://www.vias.org/simulations/simusoft_blackbody.html

Examples

Planck’s distribution law above was expressed in terms of frequency. Express Planck’s radiation law in terms of wavelength .

Examples

Planck’s distribution law above was expressed in terms of frequency. Express Planck’s radiation law in terms of wavelength .

Solution:

Because v and are related by =c, d=-c d/2. If we substitute d = -c d/2 into Planck’s distribution law,

1

8),(

/5

kThce

dhcdT

The quantity (,T)d is the energy density between and +d .

1.3

Blackbody radiation

A plot of the intensity of blackbody radiation versus frequency for several temperature

Einstein explained the photoelectric effect with a quantum hypothesis

Albert Einstain

1879-1955

Photoelectric effect

Emission of electron from metal plate

The photoelectric effect is a quantum electronic phenomenon in which electrons are emitted from matter after the absorption of energy from electromagnetic radiation such as x-rays or visible light. The emitted electrons can be referred to as photoelectrons in this context. The effect is also termed the Hertz Effect, due to its discovery by Heinrich Rudolf Hertz.

Photoelectric effectEnergy of photon = Energy needed to remove an electron + Kinetic energy of the emitted electron

2

2

1mvhv

is the work function of the metal, is similar to an ionization energy.

1.4

The kinetic energy cannot be negative, so Eq 1.4 predict that hv

The minimum frequency that will reject an electron is just the frequency required to overcome the work function of the metal and it is a threshold frequency vo

ohv 1.5

Photoelectric effect

How to measure the kinetic energies of electron? If the electrons are directed toward a negatively charged

electrode, then they will slow down because they are working against the electrical potential . If the potential is continously increased , the electrons eventually will be stpped completely, and the potential to do this is called the stopping potential. At the stopping potential, the initial kinetic energy of the electron is equal to the potential energy

seVmv 22

1

where Vs is the stopping potential

2

2

1mvhv

ohv

seVmv 22

1

os hvhveV This equation shows that a plot of Vs versus v should be linear, in complete agreement with the experimental data and the slope of the line should be h/-e

Photoelectric effect

Photoelectric effect

How to express the work function, in energy units of electron volts (eV)?

Photoelectric effect

How to express the work function, in energy units of electron volts (eV)?One electron volt is the energy that a particle with the same charge as an electron (or a proton) picks up when it falls through a potential drop of one volt. (1 coulomb x 1 volt= 1 joule)1eV = (1.602x10-19C)(1V) = 1.602x10-

19J

Example:

Given that the work function for sodium metal is 1.82 ev, what is the threshold frequency vo for sodium?

Example:

Given that the work function for sodium metal is 1.82 ev, what is the threshold frequency vo for sodium?

Solution:Convert from electron volts to joules

JxeV

JxeVeV 19

19

1092.2)10602.1

)(82.1(82.1

ohvUse

HzxsxJsx

Jxvo

1411434

19

1040.41040.410626.6

1092.2

Example

When lithium is irradiated with light, one finds a stopping potential of 1.83 V for =3000Å and 0.80 V for =4000 Å. From these data and the known charge on the electron, calculate (a) Planck’s constant, (b) the threshold potential, and © the work function of lithium

Solution (a):

JsxCxJsCxh

JsCxHzx

V

e

h

hHzxVVe

hcvvhhvhveV

VVeeV

oos

s

3419115

1

14

14

21

21

1063.6)10602.1)(1014.4(

151014.41049.2

03.1

)1049.2()80.083.1(

)11

()(

)(

Solution (b):

Using the = 3000Å data

Hzxv

hvmx

hcVCx

o

o

14

719

1057.5

1000.3)83.1)(10602.1(

Solution (c):

ohv

eVJx 30.21069.3 19

Conclusions

Using the known value of e, Einstain obtained a value of h in close agreement with Planck’s value deduced from the blackbody radiation formula.In two very different set of experiments, blackbody radiation and photoelectric effect, the very same quantization constant, h arose naturally

Problems

1. At what wavelength does the maximum in the energy-density distribution function for a black body occur if (a) T=300K? (b) T=3000K? (c) T=10,000 K?

2. Sirius, one of the hottest known stars, has approximately a blackbody spectrum with max=2600. Estimate the surface temperature of Sirius

Problems

3. Given that work function of chromium is 4.40 eV, calculate the kinetic energy of electrons emitted from a chromium surface when it is irradiated with ultraviolet radiation of wavelength 2000A. What is the stopping potential for these electrons?

Problems

4. When a clean surface of silver is irradiated with light of wavelength 230 nm, the stopping potential of the ejected electrons is found to be 0.80 V. Calculate the work function and the threshold frequency of silver

Wien's Displacement Law Wien's displacement law is a law of physics that states that there is an

inverse relationship between the wavelength of the peak of the emission of a black body and its temperature. lmax = 0.002898 / T

where T is the temperature of the black body in kelvin (K) and lmax is the peak wavelength in meters. The 0.002898 is a proportionality constant with units m×K.

Basically, the hotter an object is, the shorter the wavelength at which it will emit radiation. For example, the surface temperature of the sun is 5780 K, giving a peak at 500 nm. This is fairly in the middle of the visual spectrum, due to the spread resulting in white light. Due to the Rayleigh scattering of blue light by the atmosphere this white light is separated somewhat, resulting in a blue sky and a yellow sun. A lightbulb has a glowing wire with a somewhat lower temperature, resulting in yellow light, and something that is "red hot" is again a little less hot.

Although the law was first formulated by Wilhelm Wien, today we it derive it from Planck's law of black body radiation.

Hydrogen Atomic Spectrum

Bohr’s theory of the structure of the hydrogen atom

H

Hg

Ne

Johann Balmer, 1885

Where n = 3,4,5,…