1 out of 3 attempts Consider the following energy levels of a hypothetical atom:

Question

1 out of 3 attempts Consider the following energy levels of a hypothetical atom: 1.61 x 10 19 J 5.81 x 10 19 J 1.25 x 10 18 EI 1.65 x 10 18 J (a) What is the wavelength of the photon needed to excite an electron from E1 to E4? x 10 (b) What is the energy (in joules) a photon must have in order to excite an electron from E2 to E x 10 (c) When an electron drops from the E3 level to the E1 level, the atom is said to undergo emission. Calculate the wavelength of the photon emitted in this process Assistance Check My Work View Hint View Question Show Me Guided Solution Print Question Help Report a Problem

Explanation / Answer

Solution :-

a). wavelength needed to E1 to E4

lets find the difference in the energies of the E1 and E4

delta E = -1.61*10^-19 J –(-1.65*10^-18 J) = 1.489*10^-18 J

now lets calculate the wavelength

E=hc/l

hc/E= l

6.626*10^-34 J.s * 3*10^8 m per s / 1.489*10^-18 J = l

1.33*10^-7 m = l

So the wavelength is 1.33*10^-7 m

b) energy needed E2 to E3

lets find the difference in the energy

delta E = E3-E2

           = -5.81*10^-19 J – (-1.25*10^-18 J)

           = 6.69*10^-19 J

So the photon must have energy 6.69*10^-19 J

c) wavelength when photon drops from E3 to E1

delta E = E2-E3

           = -1.25*10^-18 J – (-1.61*10^-19 J)

          = -1.089*10^-18 J

Now lets calculate the wavelength

E=hc/l

hc/E= l

6.626*10^-34 J.s * 3*10^8 m per s/1.089*10^-18 J = l

1.83*10^-7 m = l

So the wavelength is 1.83*10^-7 m

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