A cathode ray tube uses a potential difference of 5.0 kV to accelerate electrons and produce an electron beam that makes images on a phosphor screen. What is the speed of these electrons as a percentage of the speed of light? multiple choice0.025%0.22%1.3%4.5%14%25%
Question
A cathode ray tube uses a potential difference of 5.0 kV to accelerate electrons and produce an electron beam that makes images on a phosphor screen. What is the speed of these electrons as a percentage of the speed of light? multiple choice0.025%0.22%1.3%4.5%14%25%
Solution
To solve this problem, we first need to understand that the kinetic energy (KE) of the accelerated electrons is equal to the electrical energy provided by the potential difference. This can be expressed as:
KE = qV
where q is the charge of an electron (1.6 x 10^-19 C) and V is the potential difference (5.0 kV or 5000 V).
So, KE = 1.6 x 10^-19 C * 5000 V = 8 x 10^-16 J
The kinetic energy can also be expressed in terms of mass (m) and velocity (v) as:
KE = 1/2 mv^2
We can equate the two expressions for KE and solve for v:
8 x 10^-16 J = 1/2 * 9.11 x 10^-31 kg * v^2
Solving for v gives us v = 4.19 x 10^7 m/s.
The speed of light (c) is approximately 3 x 10^8 m/s. To find the speed of the electrons as a percentage of the speed of light, we divide the speed of the electrons by the speed of light and multiply by 100:
(4.19 x 10^7 m/s) / (3 x 10^8 m/s) * 100 = 13.97%
So, the speed of the electrons is approximately 14% the speed of light. Therefore, the correct answer is 14%.
Similar Questions
calculate the velocity of the electron as a percentage of the speed of light.round your answer to the first decimal place.
The diagram below represents a cathode ray tube in which electrons emitted from the hot filament are accelerated towards the positively charged screen. The electric field in the evacuated space between the screen and filament has a constant magnitude of 105 Vm-1. The speed of the electrons on reaching the screen is:Select one:a.8.4x107 ms-1.b.1.8x1016 ms-1.c.2.0x103 ms-1.d.1.0x104 ms-1.e.3.7x106 ms-1.Clear my choice
Electrons emitted from the cathode of a cathode ray tube are accelerated by a potentialdifference of 2.00 kV between the cathode and the anode. The electrons then enter the uniformelectric field between the middle of two parallel conducting plates, each of length 2.00 cm. ThePotential difference between the plates is 500 V and the plates are separated by a distance of1.50 cm.Calculate(a) the velocity 𝑢 of the electrons when they emerge from the anode.(b) the time taken for the electrons to transverse the uniform electric field.(c) the velocity of the electrons when they emerge from the uniform electric field.
An electron is accelerated from rest between two parallel plates that are seperated by 2.20 cm. The potential difference between the two plates is 2.10×103 V. If the electron travels from the negative plate to the positive plate, what will be the speed of the electron as it exits through a small hole in the positive plate? 2.72×107 m/s 2.20×107 m/s 3.24×107 m/s 4.03×106 m/s
Calculate the speed achieved by an electron accelerated in a vacuum through a p.d of 2000 V. (5 marks)
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.