(a) Consider the following three statements: (i) A hydrogen atom in the n = 3 state can emit light at only two specific wavelengths, (ii) a hydrogen atom in the n = 2 state is at a lower energy than the n = 1 state, and (iii) the energy of an emitted photon equals the energy difference of the two states involved in the emission. Which of these statements is or are true? (b) Does a hydrogen atom “expand” or “contract” as it moves from its ground state to an excited state?

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Elin HesselLv2

23 May 2020

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1. An atom, X, has a ground state binding energy(energy necessary to eject electron from the ground state) of 2.179e-18 J. The line(emission) spectrum for atom X is shown with n=2 to n=1(121.57 nm), n=3 to n=1(102.57 nm), n=4 to n=1(97.254 nm), n=5 to n=1(94.974 nm),and n=6 to n=1(93.780 nm). For each of the emission lines(given as wavelengths in nm), the final state is the ground state, or lowest energy state, of the atom.

a. What is the energy of the third excited state of X?

b. What is the energy of the highest energy state of X that is necessary to account for the emission spectrum?

c. Is it possible for an electron in the ground state of atom X to absorb light of energy 3.03e-19 J? Why or why not?

d. Can atom X emit light of energy 3.03e-19 J? If so, what are the initial and final states of such a transition?

e. Is it possible for X to absorb light of energy 2.5e-18 J? Why or why not?

Anelectron in an excited state of a hydrogen atom emits two photonsin succession, the first at 486.0 nm and the second at 121.5 nm, toreturn to the ground state (n=1). For a given transition, thewavelength of the emitted photon corresponds to the difference inenergy between the two energy levels.

What werethe principal quantum numbers of the initial and intermediateexcited states involved?

(Enter thenumber of the higher atomic orbital in the first answerbox.)

initialexcited state

intermediateexcited state

Need all four answered please.