A negatively charged oil drop with unknown mass is observed between two horizontal parallel metal plates with the distance $d=12\:mm$ in Millikan's experiment. The droplet falls vertical at its terminal speed. By timing 1 minute, the drop falls 1 cm. The viscosity of air is $\eta_{air}=17.1\cdot 10^{-6}\:kg/(ms)$. The density of the oil is $\rho=855\:kg/m^3$.
If two forces balance, the oil drop is held stationary.
$Q$ | $e$ | $2e$ | $3e$ | $4e$ |
$V$ in V | 5 | 10 | 15 | 20 |
Author: J. Blum, D. Supper, CDSC
The retarding potential method is used to determine Planck's constant $h$.
color | $f$ in $10^{14}\:$Hz | voltage in V |
yellow | 5.19 | 0.15 |
green | 5.5 | 0.3 |
blue | 6.88 | 0.9 |
violet | 7.41 | 1.1 |
element | Ag | Cu | Al | Si |
$\Phi$ in eV | 4.7 | 4.48 | 4.2 | 3.59 |
Calculate the threshold frequency $f_0$ and the corresponding cut-off wavelength $\lambda_0$ for each element.
element | Ag | Cu | Al | Si |
$\Phi$ in eV | 4.7 | 4.48 | 4.2 | 3.59 |
$f_0$ in $10^{14}$ Hz | 11.5 | 11.0 | 10.3 | 8.81 |
$\lambda_0$ in nm | 261 | 273 | 291 | 340 |
Materials:
Procedure:
color | blue | green | red |
wavelength $\lambda$ in nm | 465 | ... | ... |
frequency $f$ in $10^{14}$ Hz | ... | ... | ... |
$E=eV_{th}$ | ... | ... | ... |
possible experimental values:
color | blue | green | yellow | red | dark red | infrared |
wavelength $\lambda$ in nm | 465 | 560 | 585 | 635 | 660 | 950 |
frequency $f$ in $10^{14}$ Hz | ||||||
$E=eV_{th}$ in $eV$ | 2.7 | 1.69 | 1.62 | 1.51 | 1.51 | 1.1 |
Calculate the energy of the photons in $eV$ and $J$ for the following electro-magnetic radiation:
After thermionic emission electrons are accelerated with $30\:keV$ and $50\:keV$ hitting the target.
For measuring the different wavelength we use the Bragg grating with a LIF-crystal (lithium fluoride). The crystal has a grating constant of $d=2.014 \cdot 10^{-10}\:m$.
Thermionic emission | if a low voltage heats a cathode, electrons can escape the surface |
electron-volt, eV | a energy unit for small particles: $1\:\text{eV}=1.6\cdot 10^{-19}\:\text{J}$. |
Millikan's experiment | an experiment from Robert Millikan to determine the elementary charge of an electron $e=1.602\cdot 10^{-19}\:\text{C}$ |
photo-electric effect | free emitted electrons through light |
Planck's equation | $E_{Ph}=h\cdot f$ with Planck's constant $h=6.6\cdot 10^{-34}\:\text{Js} |
photon | Light is made of tiny particles, quantums called photons. Each Photon has a certain energy which can be calculated by Planck's equation. |
Einstein's equation | The energy needed to liberate electrons from a metal surface is called the work function $\Phi$. The kinetic energy of the electron is calculated by the energy of the photon $hf$ with Einstein's equation: $E_{kin}=hf - \Phi$. |
X-rays | X-rays (X-radiation) are electromagnetic waves. They are produced when high-speed electrons decelerate quickly. The frequency range is from $3\cdot 10^{16}\:$Hz to $3\cdot 10^{19}\:$Hz, with a corresponding wavelength of 0.01 to 10 nm. |
Wilhelm Conrad Röntgen | German scientist who discovered in 1985 and named it X-radiation to signify an unknown type of radiation. |
minimum wavelength of X-rays | The minimum wavelength or cutoff wavelength $\lambda_{min}$ corresponds to the maximum frequency $f_0$ of X-radiation |
continuous x-ray spectrum | Electrons are scattered on atoms, some losing their total incident kinetic energy ($\lambda_{min}$), some only partly to X-ray photons. |
characteristic x-ray spectrum | The electrons collide with an atom of the target knocking out one of the most internal electrons of the atom. |