Consider a Bohr model of doubly ionized lithium. (a) Write an expression similar

Question

Consider a Bohr model of doubly ionized lithium.
(a) Write an expression similar to En = -13.6 eV/n2 ? E2 = -13.6 eV/22 = -3.40 eV for the energy levels of the sole remaining electron. (Use the following as necessary: n.)
En = eV

(b) Find the energy corresponding to n = 4.

Your response differs from the correct answer by more than 10%. Double check your calculations. eV

(c) Find the energy corresponding to n = 1.

Your response differs from the correct answer by more than 10%. Double check your calculations. eV

(d) Calculate the energy of the photon emitted when the electron transits from the fourth energy level to the first energy level. Express the answer both in electron volts and in joules.
eV
J

(e) Find the frequency and wavelength of the emitted photon.
Hz
nm


please help!

Explanation / Answer

for lithium z =3

(a) En = - Z^2 (13.6 eV ) / n^2

(b) for n=8 ,

E8 = - (3)^2 (13.6 eV ) / (8)^2 = -1.9125 eV or -1.91 eV

(c) for n=2

E2 = - (3)^2 (13.6 eV ) / (2)^2 = -30.6 eV

(d) E = E8 - E2 = - 1.9125 eV + 30.6 eV = 28.6875 eV or 28.7 eV

in Joules E =  28.6875 (1.6*10^-19 J) = 4.59*10^-18 J

(e) wavelength f = hc / E

= ( 6.63*10^-34 js )(3*10^8 m/s) / 4.59*10^-18 J = 43.33 nm

frequency f = E /h = 4.59*10^-18 J / ( 6.63*10^-34 js )

= 6.923*10^15 Hz

(f) ultraviolet region

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