The "seeing" ability or resolution of radiation is determined by its wavelength.If the size of an atom is approximately 10^-10 m,how fast must an electron travel to have a wavelength smaller than that of an atom? (m_e = 9.11 x 10^-31 kg and h = 6.63 x 10^-34 J*s) A)7.3 x 10⁶ m/s B)3.4 x 10⁶ m/s C)1.0 x 10⁶ m/s D)5.4 x 10⁵ m/s

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Quizplus · Accepted Answer

The de Broglie wavelength of an electron is given by λ = h/p, where p is the momentum of the electron. To have a wavelength smaller than that of an atom (10^-10 m), we need λ < 10^-10 m. Therefore, λ = h/p < 10^-10 m => p > h/10^-10 m = 6.63 x 10^-25 kg m/s The momentum of an electron is given by p = mv, where m is the mass of the electron and v is its speed. Therefore, v = p/m > (h/10^-10 m)/9.11 x 10^-31 kg => v > 7.27 x 10^6 m/s Therefore, the electron must travel at a speed greater than 7.27 x 10^6 m/s to have a wavelength smaller than that of an atom. The closest answer choice is A) 7.3 x 10^16 m/s.

The "Seeing" Ability or Resolution of Radiation Is Determined by Its