An electron of mass m and a photon have same energy E. The ratio of wavelength of electron to that of photon is: (c being the velocity of light)
An electron of mass m and a photon have same energy E. The ratio of wavelength of electron to that of photon is: (c being the velocity of light)
Option 1 -
(1/c) * (E / 2m)¹/²
Option 2 -
(E / 2m)¹/²
Option 3 -
c(2mE)¹/²
Option 4 -
(1/c) * (2m / E)¹/²
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1 Answer
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Correct Option - 2
Detailed Solution:The relationship between the de Broglie wavelengths of an electron (λe) and a photon (λp) is derived as follows:
For an electron: λe = h / mv = h / √ (2mE)
For a photon: λp = h / p = hc / ETaking the ratio of the wavelengths squared:
(λe / λp)² = [h / √ (2mE)]² / [hc / E]²
(λe / λp)² = (h² / 2mE) * (E² / h²c²)
(λe / λp)² = E / 2mc²
(λe / λp) = (1/c) * √ (E / 2m)
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