Electrons are emitted from metals during photoelectric emission, thermionic emission and radioactive decay - Leaving Cert Physics - Question 8 - 2019

The electrons emitted during radioactive decay are called beta particles.

A line emission spectrum is produced when an element emits light of specific wavelengths, resulting in distinct lines on a spectrum.

This occurs in an atom when electrons transition between energy levels. When an electron moves from a higher energy level to a lower energy level, it emits a photon of light. The emitted photon corresponds to a specific energy difference between the two levels, leading to a specific wavelength.

Einstein's photoelectric equation is given by:

$E_k = hf - ext{Work Function}$

where $E_k$ is the kinetic energy of the emitted electron, $h$ is Planck's constant, and $f$ is the frequency of the incident light.

(i) Point A represents the threshold frequency, which is the minimum frequency needed to eject electrons from the metal surface.

(ii) The slope of the graph represents Planck's constant (h), indicating the relationship between the kinetic energy of emitted electrons and the frequency of the incident radiation.

First, we calculate the kinetic energy of the emitted electrons using the photoelectric equation.

Since the work function of magnesium is 3.68 eV:

$E_k = 4.15 ext{ eV} - 3.68 ext{ eV} = 0.47 ext{ eV}$.

To find the maximum velocity, we convert kinetic energy into joules:

E_k = rac{1}{2}mv^2

where $m$ is the mass of the electron, approximately $9.1 imes 10^{-31} ext{ kg}$.

Rearranging gives:

v = ext{sqrt}igg(rac{2E_k}{m}igg = ext{sqrt}igg(rac{2 imes 0.47 imes 1.6 imes 10^{-19}}{9.1 imes 10^{-31}}igg

Calculating yields the maximum velocity of the emitted electrons.

Electrons are produced at the cathode in the X-ray tube.

The minimum wavelength of an X-ray can be calculated using the equation:

ext{Energy} = rac{hc}{ ext{wavelength}}

For a 50 kV tube, the energy of the X-ray is 50 keV, which can be converted to joules, and we use Planck's constant (h) and the speed of light (c) to find the wavelength.

1. Tungsten target: The tungsten target is used due to its high atomic number, which increases the efficiency of X-ray production.

2. Cooling fluid: A cooling fluid is used in the X-ray tube to dissipate the heat generated by the electrons colliding with the target.