Hydrogen discharge question

[nateastle]

I have been trying to figure out what the equation is for this problem:

A glass tube filled with gas has electrodes at each end. When a sufficiently high potential difference is applied between the two electrodes the gas ionizes; electrons move towards the positive electrod, and the positive ions move toward the negative electrode. a) What is the current in a hydrogen discharge if, in each second, 3.6 * 10 ^18 electrons and 1.15 * 10 ^18 protons move in the oppisite directions through a cross section of the tube?

I am not sure what the equation(s) is to solve this problem. I have searched my book to see if I can find something similar to this but have not been able to find anything that discusses this topic.

 

[Astronuc]

Current is the charge (moving) per unit time.

The current in this case is composed of negative charges (electrons) and positive charges (protons), which move more slowly since they are heavier.

By convention, the current is in the direction of the movement of positive charge, which means in the direction of proton movement, and opposite the direction of the electron movement.

I = (n_p*q_p - n_e*q_e)/ 1 sec.

The - sign before the electron contribution indicates that the electrons are moving opposite the protons. The charge on the q<sub>e[/sup] = -qp.

np = number of protons, ne = number of electrons

and q = magnitude of charge of the proton (+) and electron (-)</sub>

 

[kyle8921]

The equation you are looking for is the current equation, which is defined as the rate of flow of electric charge. It is represented by the symbol I and is measured in amperes (A). The equation for current is I = Q/t, where Q is the total charge that passes through a given cross section in a certain amount of time t. In this case, we can use the values given in the problem to calculate the current.

First, we need to find the total charge that passes through the cross section in one second. We know that 3.6 * 10 ^18 electrons and 1.15 * 10 ^18 protons move in opposite directions, so the total charge is the sum of the charge of the electrons and the protons. The charge of an electron is -1.6 * 10 ^-19 coulombs (C) and the charge of a proton is +1.6 * 10 ^-19 C. Therefore, the total charge is (3.6 * 10 ^18 * -1.6 * 10 ^-19) + (1.15 * 10 ^18 * 1.6 * 10 ^-19) = -5.76 * 10^-1 + 1.84 * 10^-1 = -3.92 * 10^-1 C.

Next, we need to find the time t. The problem states that the charge passes through the cross section in one second, so t = 1 second.

Now, we can plug these values into the current equation: I = Q/t = (-3.92 * 10^-1 C) / (1 second) = -3.92 * 10^-1 A. However, since current is a scalar quantity, we can ignore the negative sign and simply state that the current in the hydrogen discharge is 3.92 * 10^-1 A.

I hope this helps you solve the problem and understand the concept of current in a hydrogen discharge. If you have any further questions, please let me know.