Calculating e/m Ratio: Step-by-Step Guide for Accurate Results

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In summary, the e/m ratio, or charge-to-mass ratio, is a fundamental property of charged particles used to understand their behavior in electromagnetic fields. To accurately calculate it, a cathode ray tube, power supply, magnetic field source, voltmeter, and ruler/micrometer are needed. The process involves setting up equipment, creating a vacuum, measuring values, and using a formula. Common sources of error include inaccurate measurements and external interference. The e/m ratio has various applications in scientific research, including particle physics, electromagnetism, and the development of new technologies.
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barcelonaboy
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Homework Statement



I'm trying to calculate the charge ratio of e/m, I've plotted the given data points to get a straight line graph with a gradient of 0.848.



Homework Equations



I know that I can calulcate the charge ratio of e/m by using
e/m = (4.49*10^8 * gradient^2)/volts

where volts = 3000.

The Attempt at a Solution



When I plug the numbers in I get a value of 107625 which is nowhere near the given book value of e/m 1.7*10^11 Ckg^-1

I think that I'm doing something in the wrong units as I need to get the answer in C/kg^-1, but I can't see where I'm going wrong.

Any pointers would be much appreciated
 
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it is important to always check your units and ensure they are consistent throughout your calculations. In this case, it seems like you are using the correct equation but may have made a mistake in converting units.

First, let's look at the units for e/m. The unit for e/m is C/kg^-1, which means Coulombs per kilogram. This tells us that the unit for e/m should be in terms of charge per unit mass.

Next, let's look at the units for the given data points. The gradient is given in terms of meters per second squared (m/s^2). However, in order to use the equation, we need to convert this to units of volts. This can be done by multiplying the gradient by the distance between the plates (in meters) and dividing by the voltage (in volts). This will give us units of volts/meter, which is the correct unit for the gradient in this equation.

Now, let's look at the units for the voltage. The given voltage is 3000 volts, which is the correct unit for voltage. However, in order to use this in the equation, we need to convert it to units of meters. This can be done by multiplying the voltage by the distance between the plates (in meters) and dividing by the gradient (in m/s^2). This will give us units of meters, which is the correct unit for voltage in this equation.

Finally, let's put everything together. We have the gradient in units of volts/meter, the voltage in units of meters, and the given value for e/m in units of C/kg^-1. When we plug these into the equation, we get a value for e/m in units of C/kg^-1, which is consistent with the given book value.

In summary, it is important to always check your units and make sure they are consistent throughout your calculations. In this case, the mistake was most likely a unit conversion error. By double checking your units, you can ensure that your final answer is in the correct units and accurately reflects the given data.
 

What is the purpose of calculating e/m ratio?

The e/m ratio, also known as the charge-to-mass ratio, is a fundamental property of charged particles. It is used to determine the specific charge of an electron, which is essential for understanding the behavior of particles in electromagnetic fields.

What materials and equipment are needed to calculate e/m ratio?

To accurately calculate e/m ratio, you will need a cathode ray tube (CRT), a power supply, a magnetic field source, a voltmeter, and a ruler or micrometer. You will also need to create a vacuum in the CRT to ensure accurate results.

What is the step-by-step process for calculating e/m ratio?

The first step is to set up the equipment and create a vacuum in the CRT. Then, you will need to measure the radius and length of the CRT and the strength of the magnetic field. Next, you will use the power supply to vary the voltage and observe the deflection of the electron beam on the CRT. Finally, you can use the measured values to calculate the e/m ratio using the formula e/m = (Vd/B^2)(8L/R^2), where Vd is the voltage, B is the magnetic field strength, L is the length of the CRT, and R is the radius of the CRT.

What are some common sources of error when calculating e/m ratio?

Some common sources of error include inaccurate measurements of the CRT dimensions and magnetic field strength, poor vacuum in the CRT, and external electrical interference. It is essential to carefully calibrate and double-check all measurements to minimize these errors.

What are the applications of e/m ratio in scientific research?

The e/m ratio has many applications in scientific research, particularly in the fields of particle physics and electromagnetism. It is used to study the behavior of charged particles in electric and magnetic fields, as well as to determine the properties of subatomic particles. It is also used in the development of new technologies, such as particle accelerators and mass spectrometers.

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