# Application of Virtual Reality in Learning Quantum Mechanics
## 2 Virtual Teaching Modules
### Cathode-Ray Tube Experiment  
A cathode-ray tube is a vacuum glass enclosure containing an electron gun, an electron source, and a fluorescent wall. The electrons can be accelerated and redirected by an internal or external voltage. When the electrons hit the fluorescent wall, a light spot is generated. Electrons are accelerated by an electric field in the cathode-ray tube from one end to the other. When the electrons hit the fluorescent wall, the kinetic energy is converted into heat and X-rays. This study used 3 ds Max to build the 3D model of the cathode-ray tube and then used C# in Unity 3D to design the user-interface programs for changing the voltage of the electric field to control the deflection of electrons.  
When using the virtual teaching module, the user first removes the gas in the cathode ray tube to reduce the pressure, and connects two metal pieces with high voltage to ionize the air and make it an electrical conductor, and then connects the metal pieces at both ends of the glass tube to an external voltage to accelerate electrons from one end to the other. After the cathode is heated, the electrons released by the electric field quickly move to the positive electrode. The electrons passing through the anode will hit the phosphorescent material on the tube wall to generate a light spot. In order to identify the passage of the electron beam, the user can install the positive and negative electrodes of the electric field on the lower and upper sides of the cathode ray tube separately and apply a voltage for deflecting the electrons. The electron beam will be repelled by the negative electrode and deflected to the positive electrode. The user can observe how the fluorescent light is deflected downward to understand that the particles of the cathode-ray tube are negatively charged (Figure 2). A magnetic field can also be used to balance the force on the electrons for the calculation of its mass-to-charge ratio.  
Figure 2: Virtual cathode-ray tube experiment.  
If the learner applies a magnetic field \(B\) in the direction perpendicular to the electric field of the cathode-ray tube, the electrons will move in a circular motion under the action of the magnetic field when the electric field stops acting as described below, according to [PERSON]'s second law of motion.  
\[F=qvB=ma_{r}=\frac{mv^{2}}{r} \tag{1}\]  
In the above formula, the radius of the circular motion of the electron can be calculated as  
\[r=\frac{mv}{qB} \tag{2}\]  
If the magnetic field \(B\) and electric field \(E\) are adjusted so that the electrons are not deflected, it means the magnetic force is equal to the electric force, i.e.,  
\[F_{B}=qvB=F_{E}=qE \tag{3}\]  
After eliminating the charge q in the above equations, the velocity of the electron can be calculated as  
\[v=\frac{E}{B} \tag{4}\]  
By balancing the magnetic force and electric force, we can calculate the velocity v of the electron and then use the equation of the circular motion to find the mass-to-charge ratio of the electron using the following equation  
\[\frac{q}{m}=\frac{v}{rB} \tag{5}\]  
In this study, the virtual experiment allows learners to ionize the air using a high voltage to make it an electrical conductor and adjust the electric and magnetic fields to balance the force on the electron so that it will not be deflected, and then calculate the mass-to-charge ratio of the electron according to the above formula. They can continue with the oil drop experiment to calculate the charge and mass of electrons.