The cathode-ray tubes that generated the picture in early color televisions were sources of x rays. If the acceleration voltage in a television tube is 15.0 kV, what are the shortest-wavelength x rays produced by the television?

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Hi everyone. In this practice problem, we will have Rangan tubes which are evacuated electron tubes used to produce x-rays. We're being asked to determine the shortest wavelength of the x-rays produced if the accelerating potential inside of the tube is 17 kg fault. The options given are a 0.117 nanometer B 0.731 nanometer C 0. nanometer and lastly D 0.731 nanometer, we want to recall that the increase in the accelerating potential inside the tube gives the energy to the electrons which is then imparted to photons producing x-rays energy or E can be calculated by multiplying H with C and dividing dividing that with lambda where H is the Plank's constant, which is 6.63 times 10 to the power of negative GS and C is just the speed of light which is 3. times 10 to the power of eight m per second. Lambda is just going to be the wavelength. And at the same time energy or E can also be calculated by multiplying E with V where E is just the charge of an electron and V is the accelerating voltage E is also a constant, which is 1.6 times 10 to the power of negative 19 coon. So we can actually combine the first equation and the second equation. So we can equal E um equate both E or both energy. So that we get H C divided by a lambda to be equals to E multiplied by V. We are interested to find the shortest wavelength. So we are interested to find the lambda. So we wanna rearrange this equation so that we get an equation for lambda to then be equals to H C divided by E V. So now we can actually in uh input all of the information that we know because we know what the H C and E are because all of those are just constants and the fat is given or the potential is given in the problem statement which is 17 kg fold. So then lambda will then equals to H C divided by E V. H is uh 6.63 times 10 to the power of negative 34 Jules seconds. C is 3.0 times 10 to the power of eight m per second. And E is off that is going to be divided by E which is 1.6 times 10 to the power of negative 19 colon. And the voltage is 17 kg fold. We wanna convert that into fold So multiply 17 with 10 to the power of three to get fault. So then doing this calculation, we will then get the lambda to then be equal to 0.7312 times 10 to the power of negative 10 m. Or converting that into nanometer, we will have to multiply this but 10 to the power of nine nanometer for every one m which will then give us a lambda value of 0.731 nanometer. So the shortest wavelength of the x-rays produced if the accelerating potential inside the tube is 17 kg fold is going to be 0.731 nanometer which will correspond to option D in our answer choices. So option D will be the answer to this particular practice problem and that'll be it for this video. If you guys still have any sort of confusion, please make sure to check out a lesson videos on similar topics on our website. But other than that, that will be it for this one. Thank you.

The cathode-ray tubes that generated the picture in early color televisions were sources of x rays. If the acceleration voltage in a television tube is 15.0 kV, what are the shortest-wavelength x rays produced by the television?

Verified Solution

Key Concepts

X-ray Production

Wavelength and Energy Relationship

Acceleration Voltage