Electrons accelerated by a potential difference of 12.11 Vpass through a gas of

Question

Electrons accelerated by a potential difference of 12.11 Vpass through a gas of hydrogen atoms at room temperature.
A)Calculate the wavelength of light emitted with the longestpossible wavelength.
B)Calculate the wavelength of light emitted with the shortestpossible wavelength. Electrons accelerated by a potential difference of 12.11 Vpass through a gas of hydrogen atoms at room temperature.
A)Calculate the wavelength of light emitted with the longestpossible wavelength.
B)Calculate the wavelength of light emitted with the shortestpossible wavelength.

Explanation / Answer

A)the energy of the electrons when they pass through the gasof hydrogen atoms at room temperature is E = K - En K = e * V where e is the charge on the electron and V is thepotential difference En = -(13.6/n2) eV where n is theprincipal quantum number 1 eV = 1.6 * 10-19 J or En = -(13.6/n2) * 1.6 *10-19 J or E = e * V - (-(13.6/n2) * 1.6 *10-19) = e * V + ((13.6/n2) * 1.6 *10-19) or (h * c/) = e * V + ((13.6/n2) * 1.6 *10-19) or = [h * c/e * V + ((13.6/n2) * 1.6 *10-19)] for the longest possible wavelength we have n = therefore we get = [h * c/e * V + ((13.6/()2) * 1.6 *10-19)] = (h * c/e * V) e = 1.6 * 10-19 C and V = 12.11 V B)for the shortest possible wavelength we have n = 1 or = [h * c/e * V + ((13.6/(1)2) * 1.6 *10-19)] = [h * c/e * V + ((13.6 * 1.6 *10-19)] K = e * V where e is the charge on the electron and V is thepotential difference En = -(13.6/n2) eV where n is theprincipal quantum number 1 eV = 1.6 * 10-19 J or En = -(13.6/n2) * 1.6 *10-19 J or E = e * V - (-(13.6/n2) * 1.6 *10-19) = e * V + ((13.6/n2) * 1.6 *10-19) or (h * c/) = e * V + ((13.6/n2) * 1.6 *10-19) or = [h * c/e * V + ((13.6/n2) * 1.6 *10-19)] for the longest possible wavelength we have n = therefore we get = [h * c/e * V + ((13.6/()2) * 1.6 *10-19)] = (h * c/e * V) e = 1.6 * 10-19 C and V = 12.11 V B)for the shortest possible wavelength we have n = 1 or = [h * c/e * V + ((13.6/(1)2) * 1.6 *10-19)] = [h * c/e * V + ((13.6 * 1.6 *10-19)]

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