Minimum Wavelength of Electron Accelerated in TV at 30,000 V

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SUMMARY

The minimum wavelength of an electron accelerated through a potential difference of 30,000 V can be calculated using the equations E = qV and E = hf. The total energy of the electron is determined to be 4.8 x 10^-15 J. By manipulating the equation E = hf into E = hc/λ, the minimum wavelength can be derived, which occurs at maximum energy. This confirms that the minimum wavelength corresponds to the maximum energy of the electron as it accelerates.

PREREQUISITES
  • Understanding of basic physics concepts such as energy, voltage, and wavelength
  • Familiarity with the equations E = qV and E = hf
  • Knowledge of Planck's constant (h) and the speed of light (c)
  • Basic understanding of electron behavior in electric fields
NEXT STEPS
  • Research the implications of electron acceleration in different potential differences
  • Learn about the relationship between energy, frequency, and wavelength in quantum mechanics
  • Explore the concept of wave-particle duality and its relevance to electrons
  • Investigate applications of electron acceleration in technologies such as cathode ray tubes and particle accelerators
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Students studying physics, educators teaching quantum mechanics, and professionals in fields related to electronics and particle physics.

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Homework Statement



In a television, an electron is accelerated through a potential difference of 30,000 V. What is the minimum wavelength produced.


Homework Equations


E = qv
E = hf

The Attempt at a Solution



I figured that we should first find total energy.
E = qv => E = (1 x 10^-16)(30,000) = 4.8 x 10^-15

Then I can manipulate the equation E = hf into E = hc/(lambda) to find the wavelength.
I'm not sure if solving this equation will yield the minimum wavelength or the maximum wavelength. What is the case and why?
 
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the wavelength is inversely proportional to energy as you pointed out, so the minimum wavelength will be at maximum energy
 
That makes sense because frequency will be highest (and wavelength smallest) when energy is maxed.
But, assuming that I solved for maximum energy, what would be minimum energy?
 
hmmm, not too sure... but:

the electron is accelerated from close to rest across 30,000V, so it starts with very low KE, clsoe to zero and its speed increases as it accelerates in the potential difference upt a maximum at the end of the accerating region
 

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