1. An atom, X, has a ground state binding energy(energy necessary to eject elect
ID: 1024384 • Letter: 1
Question
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?
Explanation / Answer
1. From the given data for atom X,
a. Energy of the third excited state (n = 3)
Energy = hc/l
with,
h= planck's constant
c = speed of light
l = 102.57 nm = 102.57 x 10^-9 m
we get,
energy = 6.626 x 10^-34 x 3 x 10^8/102.57 x 10^-9 = 1.94 x 10^-18 J
b. Energy of the highest excited state (n = 6)
Energy = hc/l
with,
h= planck's constant
c = speed of light
l = 93.780 nm = 93.780 x 10^-9 m
we get,
energy = 6.626 x 10^-34 x 3 x 10^8/93.780 x 10^-9 = 2.12 x 10^-18 J
c. Yes, it is possible for the atom X to absorb light of energy 3.03 x 10^-19 J at ground state. The energy is lower than binding energy and thus would not eject electron from the ground state of atom X. The electron would just be in an excited state.
d. No, the atom X cannot emit light of energy 3.03 x 10^-19 J as the energy is lower than the lowest energy excited state of atom X.
e. Yes, it is possible for atom X to asborb light of energy 2.5 x 10^-18 J. This would eject an electron from the atom.
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