Q76P - Fundamentals Of Physics

Question

 A current is established in a gas discharge tube when a sufficiently high potential difference is applied across the two electrodes in the tube. The gas ionizes; electrons move toward the positive terminal and singly charged positive ions toward the negative terminal.(a)What is the current in a hydrogen discharge tube in which $\mathbf{3}\mathbf{.}\mathbf{1}\mathbf{\times }{\mathbf{10}}^{\mathbf{18}}$ electrons and $\mathbf{1}\mathbf{.}\mathbf{1}\mathbf{\times }{\mathbf{10}}^{\mathbf{18}}$ protons move past a cross-sectional area of the tube each second? (b) Is the direction of the current density $\overrightarrow{\mathbf{J}}$ toward or away from the negative terminal?

Step-by-Step Solution

Answer

1. The current in hydrogen discharge tube each second is 0.672A. 
2. The direction of the current density points towards the negative terminal.

Step 1: The given data

1. Number of electrons, $n_e=3.1\times {10}^{18}$
2. Number of protons, $n_p=1.1\times {10}^{18}$
3. Charge on electron, $q=1.60\times {10}^{-19} C$

Step 2: Understanding the concept of the flow of current and its density

In a hydrogen discharge tube, electrons are moving toward the positive terminal and then towards a negative terminal. The current flowing within a hydrogen discharge tube can be calculated by adding the electrons and protons per second moving inside it.

 

Formulae:

The current equation for total charge flow in 1 second,  i = ne                        (i) 

Step 3: a) Calculation of the current

To calculate the current in a hydrogen discharge tube per second, i.e. divided by 1 sec, we can use equation (i) with the given data as follows:

$$\begin{gathered} i=\left(3.1x{10}^{18}+1.1x{10}^{18}\right)\left(1.60x{10}^{-19}\right) \\ =0.672A \end{gathered}$$

Hence, the value of the required current each second is 0.672A.

Step 4: b) Calculation of the direction of the current density

Since the electric field points away from the positive terminal and towards the negative terminal, then the current density vector must point towards the negative terminal.