A photoelectric$-$effect experiment is designed to make use of photons that are emitted from the excited states of the hydrogen atom. The photons will strike a metal surface having a work function that is $110110$ of the ground$-$state energy of the hydrogen atom $(=|$E$1|10=|$E$1|10).$ The specific hydrogen transitions to be used are ni$>3$nf$=3$ni$>3$nf$=3.$ In terms of E$1$E$1$ and nini, determine $($a$)$ the energy of the photon that is released by the hydrogen atom when it makes a ni$$nf$=3$ni$$nf$=3$ transition; $($b$)$ the wavelength of this photon; $($c$)$ the minimum value of nini that will result in an electron being ejected from the metal surface; $($d$)$ the maximum kinetic energy of an electron that is ejected by a ni$=$$$nf$=3$ni$=$$$nf$=3$ photon.

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Part A

Write down the equation for the hydrogen atom energy levels.

Express your answer in terms of nn$,$ Planck's constant hh$,$ the speed of light cc$,$ and the Rydberg constant RR$.$

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