Question

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?

Accepted Answer

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. 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. Step 3: Perform the multiplication to find the total charge accumulated over the 2.0-hour period. Use the formula: $$ Q = 	ext{rate} 	imes 	ext{time} $$, where $$ Q  is $$the total charge, $$ 	ext{rate}  is$$ −2.0 nC/s, and $$ 	ext{time}  is $$the total time in seconds. 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. 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.

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Concetti chiave

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Current and Charge Flow

Time Conversion