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Chapter 18: Problem 6

A potential difference is applied between the electrodes in a gas discharge tube. In 1.0 s, \(3.8 \times 10^{16}\) electrons and \(1.2 \times 10^{16}\) singly charged positive ions move in opposite directions through a surface perpendicular to the length of the tube. What is the current in the tube?

Short Answer

Expert verified
Question: Find the current in the gas discharge tube given that 3.8 x 10^16 electrons and 1.2 x 10^16 singly charged positive ions move through the tube in 1.0 s. Answer: To find the current, calculate the net charge by subtracting the charge due to positive ions from the charge due to electrons, and then divide the net charge by the time interval. The current in the gas discharge tube is given by: \(I = \frac{(3.8 \times 10^{16} \times 1.6 \times 10^{-19}) - (1.2 \times 10^{16} \times 1.6 \times 10^{-19})}{1.0}\) A.

Step by step solution

01

Calculate the charge due to electrons and positive ions.

To calculate the charge due to the given number of electrons and positive ions, we need to multiply their respective numbers by the elementary charge. The elementary charge (e) is \(1.6 \times 10^{-19}\) C. Charge due to electrons = Number of electrons × Elementary charge \(Q_{e} = 3.8 \times 10^{16} \times 1.6 \times 10^{-19}\) C Charge due to positive ions = Number of positive ions × Elementary charge \(Q_{p} = 1.2 \times 10^{16} \times 1.6 \times 10^{-19}\) C
02

Calculate the net charge.

Since the electrons and positive ions move in opposite directions, we need to find the net charge that passes through the surface. To do this, subtract the charge due to the positive ions from the charge due to the electrons. Net charge = Charge due to electrons - Charge due to positive ions \(Q_{net} = Q_{e} - Q_{p}\)
03

Calculate the current.

The current (I) can be found by dividing the net charge by the time interval. The time interval (Δt) is given as 1.0 s. Current = Net charge / Time interval \(I = \frac{Q_{net}}{\Delta t}\) Now, plug in the values and compute the current: \(I = \frac{(3.8 \times 10^{16} \times 1.6 \times 10^{-19}) - (1.2 \times 10^{16} \times 1.6 \times 10^{-19})}{1.0}\) A Upon calculating the above expression, you will find the current in the gas discharge tube.

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Most popular questions from this chapter

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