Emitted from an electron gun with almost zero velocity, electrons are accelerated by an electric field E over a distance of 1.0 m . These electrons are subsequently scattered by a sample of atomic hydrogen in its ground state. Determine the minimum value of E required for the hydrogen to emit red light of wavelength 656.3 nm .

Step-by-step solution

The wavelength of the emitted red light is 656.3 nm , which corresponds to the Balmer series transition from n = 3 to n = 2 . For the hydrogen atom to emit this light, it must first be excited from its ground state ( n = 1 ) to at least the n = 3 state. The energy required for this excitation is: E = 13.6 ( 1 1^2 - 1 3^2 ) eV E = 13.6 8 9 eV 12.1 eV The kinetic energy gained by an electron accelerated by an electric field E over a distance d is given by K = eEd . To excite the hydrogen atom, the kinetic energy of t