Energy level diagram : Increasing energy: n=1 -13.59eV, n=2 -3.4 eV, n=3 -1.51 e

Question

Energy level diagram :

Increasing energy: n=1 -13.59eV, n=2 -3.4 eV, n=3 -1.51 eV, n=4 -0.85 eV, n=5 -0.54 eV,

n=6 -0.38 eV

1)      Refer to the electron energy-level diagram in the box of information for Part 2.   Include correct units and significant figures in your answers.

(a)   What is the energy difference, DE, (in eV) between the electron energy levels n=4 and n=2 in a hydrogen atom?  

(b)  What is the change in energy of the electron when it undergoes a transition from the n=4 to the n=2 energy level?   (This answer is strongly related to the answer for (a)).

c)  What is the energy (in eV) of a photon, Ephoton, that is emitted when an electron in a hydrogen atom undergoes a transition from the n=4 to the n=2 energy level?

(d)  Convert the energy of this photon from units of eV to joules.

e)  Calculate the wavelength (in nm) of this transition.  (Make sure units cancel properly in your calculation.  Check units on any constants you use.)

Explanation / Answer

a)energy difference, DE = -0.85 - (- 3.4) = 2.55 eV

b)Change in energy of electron = energy difference, DE = -0.85 - (- 3.4) = 2.55 eV or we can say final- initial = -2.55eV

c)the energy (in eV) of a photon, Ephoton = 2.55eV

d)2.55 eV= 2.55x1.6x10^(-19) J = 4.08x10^(-19) J

e)Wavelength = hc/E = 6.6x10^(-34)x3x10^(8)/[ 4.08x10^(-19)] = 485.29nm

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