An electron is trapped in a 1-dimensional box that is 576 nm wide. initially, it is in the n = 4 energy level, but after a photon is absorbed the electron is in the n = 5 energy level. what was the wavelength of the absorbed photon?

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Blacklash Blacklash · Answer 1 · 2018-09-18T21:02:58+02:00

Energy of electron in atom level n = [tex]\frac{-13.6 }{n^2} eV[/tex]

When n = 4

[tex]E_4 = \frac{-13.6}{4^2} eV = -0.85 eV[/tex]

When n = 5

[tex]E_5 = \frac{-13.6}{5^2} eV = -0.544 eV[/tex]

Energy of photon absorbed = -0.544 - (-0.85) = 0.306 eV = 0.489 * [tex]10^{-19}[/tex] J

We also have energy of photon = [tex]\frac{hc}{\lambda } = \frac{1.99*10^{-25}}{\lambda}[/tex]

Comparing both

[tex]0.489 * 10^{-19}= \frac{1.99*10^{-25}}{\lambda}\\ \\ \lambda = 4.069*10^{-6}m = 4069 nm[/tex]

So, Energy of photon = 4069 nm

okpalawalter8 okpalawalter8 · Answer 2 · 2022-04-12T12:56:54+02:00

[tex]\lamda[/tex] The wavelength of the absorbed photon is mathematically given as

[tex]\lambda[/tex]= 4069nm

Question Parameter(s):

A 1-dimensional box that is 576 nm wide

it is in the n = 4 energy level

Photon is absorbed the electron is in the n = 5 energy level

Generally, the equation for the energy of electron is mathematically given as

n = [tex]\frac{-13.6 }{n^2} eV[/tex]

E4 = -13.6/4^2

E4 = -0.85eV

E5 = -13.6/5^2

E5 = -0.544eV

energy absorbed = -0.544-(-0.85)eV

E = 0.489x 10^-19j

E = hc/lamda

0.489x10^-19 = 1.99x10^-25/landa

landa = 4,069x10^-6

lamda = 4069nm

In conclusion, the wavelength of the absorbed photon is

lambda = 4069nm