When the cathode is heated from the 6.3 V AC supply, electrons are emitted from its surface. These electrons fall on the grid (which is positive) and a current flows in the cathode/grid circuit. As electrons stream from the cathode toward the grid, they bombard atoms of the gas under study (in this case a noble gas) inside the valve. As the potential difference between the cathode and the grid is increased, electrons are accelerated through the valve at greater and greater speeds. As the kinetic energy of the electrons continues to increase, it eventually becomes great enough such that on collision with an atom, the most loosely bound electron is removed from the atom to yield a cation. The cations are attracted to the negative terminal and the electrons to the positive terminal and this leads to a sudden increase in the reading from the ammeter. The kinetic energy of the bombarding electrons can be calculated from the voltage of the system via the following formula:
How does the force exerted on the cations relate to the force exerted on the electrons given that the mass of the cation involved is 6.7 x 10-27 kg ?
AND is this a circuit + electrostatics problem? why is it causing the same force on both the cation and electron?
THANKSS!!
During the collision between electron and atom, the electron exerts a force on the atom and the atom exerts an equal and opposite force on the electron. That is Newton's third law.
The rest of the problem is about the energy required to free a bound electron from its orbit about the atom forming a positive ion flowing toward the cathode and another electron in the stream flowing toward the grid.
To understand how the force exerted on the cations relates to the force exerted on the electrons, let's first consider the basic principles involved.
1. Force and Electric Field:
In an electric field, charged particles experience a force. This force is given by the equation F = qE, where F is the force, q is the charge of the particle, and E is the electric field strength.
2. Mass and Acceleration:
According to Newton's second law (F = ma), the force on an object is directly proportional to its mass and acceleration. Therefore, for the same force, a smaller mass will experience a higher acceleration.
Now, let's analyze the situation:
In the described setup, electrons are emitted from the cathode and accelerated towards the grid by the potential difference applied between them. The electrons gain kinetic energy as they are accelerated through the valve. Once they reach the noble gas atoms, they can collide with them, causing the removal of a loosely bound electron and forming cations.
The force exerted on the cations and electrons can be related by the equation F = qE. Here, both the cations and electrons have the same charge (since they are the result of ionization of the same noble gas atom), but their masses are different (cations have a mass of 6.7 x 10^-27 kg).
As the same electric field acts on both the cations and electrons, the force they experience is the same. However, due to the difference in mass (cations being much heavier), the force on the cations will result in a lower acceleration compared to the electrons. This means that the cations will move at a slower speed compared to the electrons.
In conclusion, the force exerted on the cations and electrons is the same, as they carry the same charge. However, due to the difference in mass, the acceleration and velocity of the cations will be different from that of the electrons.
Regarding whether this is a circuit or electrostatics problem, it involves elements of both. The use of the AC supply, cathode, and grid circuit indicates a circuit-related setup. However, the acceleration and force calculations of the charged particles in the electric field involve concepts from electrostatics. So, this problem can be considered as a combination of both circuit and electrostatics principles.