Exercises: Thermionic Emission and Cathode Rays

1. a) What is thermionic emission?
2. b) Why must a metal filament be heated for it to occur?
3. c) Why must the tube be evacuated?

Cathode rays are a beam of electrons in an evacuated tube.

1. a) State two properties of cathode rays which show that they are negatively charged particles.
2. b) Name one everyday device that used cathode ray tubes.

An electron is accelerated from rest through a potential difference of $200\ \text{V}$.

1. a) Calculate the kinetic energy gained, in joules. Use $e=1.6\times10^{-19}\ \text{C}$.
2. b) State the energy in electronvolts.

In an electron gun, electrons are released from a hot cathode and accelerated by $2,500\ \text{V}$ to an anode. Use $m_e=9.11\times10^{-31}\ \text{kg}$ and $e=1.6\times10^{-19}\ \text{C}$.

1. a) Calculate the kinetic energy of each electron on reaching the anode.
2. b) Calculate the speed, using $\tfrac12 mv^2 = eV$.
3. c) Explain why the speed would be slightly less than your answer in practice, referring to the vacuum.

A beam of electrons moving horizontally at $2.0\times10^{7}\ \text{m s}^{-1}$ enters a region between two horizontal parallel plates. The upper plate is positive.

1. a) State the direction in which the beam is deflected.
2. b) The plates are $0.040\ \text{m}$ long. Calculate the time the electrons spend between them.
3. c) Explain why the path in the field is a parabola.

In a tube a beam current of $1.2\ \text{mA}$ strikes a screen.

1. a) Calculate the charge arriving at the screen in $5.0\ \text{s}$.
2. b) Calculate the number of electrons arriving in that time.
3. c) Explain what happens to the electrons' kinetic energy on impact.

Electrons are accelerated from rest through $V$ and then pass through a region of uniform magnetic field $B=1.5\times10^{-3}\ \text{T}$ perpendicular to their velocity. The path is a circle of radius $0.050\ \text{m}$. Use $m_e=9.11\times10^{-31}\ \text{kg}$, $e=1.6\times10^{-19}\ \text{C}$.

1. a) Derive an expression for the radius $r$ in terms of $m$, $v$, $e$ and $B$.
2. b) Calculate the speed of the electrons.
3. c) Calculate the accelerating voltage $V$.
4. d) Explain why the magnetic force does no work on the electrons.

Describe how thermionic emission and the properties of cathode rays were used in a J. J. Thomson-style experiment to find $e/m$.

1. a) Explain how electric and magnetic fields were balanced to find the speed of the beam.
2. b) Show that $v = E/B$ when the beam is undeflected.
3. c) Calculate $v$ if $E = 1.5\times10^{4}\ \text{V m}^{-1}$ and $B = 1.0\times10^{-3}\ \text{T}$.
4. d) Explain how the radius of the path with only the magnetic field then gives $e/m$.

A tungsten filament is heated to emit electrons which are drawn to an anode at $+300\ \text{V}$. The measured anode current is $4.0\ \text{mA}$.

1. a) Calculate the number of electrons reaching the anode per second.
2. b) Calculate the power delivered to the anode by the electron beam, assuming all kinetic energy is converted to heat.
3. c) Explain why increasing the filament temperature increases the current but increasing the anode voltage beyond a certain level does not (saturation).
4. d) State why the anode is often made of a metal with a high melting point.