A linear accelerator uses alternating electric fields to accelerate electrons to close to the speed of light. A small number of the electrons collide with a target, but a large majority pass through the target and impact a beam dump at the end of the accelerator. In one experiment the beam dump measured charge accumulating at a rate of −2.0 nC/s. How many electrons traveled down the accelerator during the 2.0 h run?

Verified step by step guidance

1. Step 1: Understand the relationship between charge and the number of electrons. The charge of a single electron is approximately −1.6 × 10⁻¹⁹ C. This means that the total charge accumulated can be used to calculate the number of electrons by dividing the total charge by the charge of a single electron.
2. Step 2: Calculate the total charge accumulated during the 2.0-hour run. Since the charge accumulates at a rate of −2.0 nC/s, multiply this rate by the total time in seconds. Convert 2.0 hours into seconds by multiplying by 3600 seconds/hour.
3. Step 3: Perform the multiplication to find the total charge accumulated over the 2.0-hour period. Use the formula: \( Q = \text{rate} imes \text{time} \), where \( Q \) is the total charge, \( \text{rate} \) is −2.0 nC/s, and \( \text{time} \) is the total time in seconds.
4. Step 4: Convert the total charge from nanocoulombs (nC) to coulombs (C). Recall that 1 nC = 10⁻⁹ C. This step ensures the units are consistent for further calculations.
5. Step 5: Divide the total charge (in coulombs) by the charge of a single electron (−1.6 × 10⁻¹⁹ C) to find the total number of electrons that traveled down the accelerator during the experiment. Use the formula: \( N = \frac{Q}{e} \), where \( N \) is the number of electrons, \( Q \) is the total charge, and \( e \) is the charge of a single electron.

Key Concepts

Charge and Electrons

Charge is a fundamental property of matter that causes it to experience a force in an electric field. Electrons carry a negative charge of approximately -1.6 x 10^-19 coulombs. Understanding the relationship between charge and the number of electrons is crucial for calculating how many electrons contribute to a given charge accumulation.

Current and Charge Flow

Electric current is the flow of electric charge, measured in amperes (A), where 1 A equals 1 coulomb per second. The rate of charge accumulation can be related to current, allowing us to determine how much charge has flowed over a specific time period. This relationship is essential for converting the charge rate into the total number of electrons.

Time Conversion

Time conversion is necessary when calculating total charge over a period. In this case, the experiment runs for 2.0 hours, which must be converted into seconds for consistency with the charge rate given in nC/s. Understanding how to convert hours into seconds is vital for accurate calculations in physics problems involving time-dependent quantities.