Question

Using the particle in a box model, the energy of the highest occupied energy level for a linear polyene of length 12 angstroms and containing 8 \text{ } \pi8 π-electrons is (m_e = 9.11 \times 10^{-31} \text{ kg}m e ​ =9.11×10 −31 kg):

Answer 1

Answer:

Using the particle in a box model, the energy of the highest occupied energy level for a linear polyene of length 12 angstroms and containing 8 \text{ } \pi8 π-electrons is (m_e = 9.11 \times 10^{-31} \text{ kg}m e =9.11×10 −31 kg):

Answer 2

Answer:

Highest occupied energy level energy = 4.178eV

Explanation:

Step - 1

Given that there are 8 π-electrons.

Filling of electrons according to the Aufbau principle

The last electron goes into the energy level,

n = 4

Step - 2

The energy of the particle in the 1-D box is given by,

$E_n = \frac{n^2h^2}{8ml^2}$

Given,

l  = 12 angstroms = $10\times 10^{-10}m$

Planck's constant, h = $6.626\times 10^{-34} m^2kg/s$

mass of electron, m = $9.11\times 10^{-31} kg$

n = 4

Calculating the energy of the highest occupied energy level -

$E_n = \frac{n^2h^2}{8ml^2} \\\\E_4 = \frac{4^2\times (6.626\times 10^{-34})^2}{8\times 9.11\times 10^{-31} \times (12\times10^{-10})^2}$

$E_4 = 0.066934\times 10^{-17} J$

Step - 3

we know that,

1 J = $6.242\times 10^{18} electronvolt$

So,

$E_4 = (0.066934\times 10^{-17})\times (6.242\times10^{18})$

$E_4 = 4.178 eV$

we got the energy of the highest occupied energy level = 4.178 eV

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