Question

• Find the lowest energy of an
electron confined to move in a one-
dimensional box of length 6 Å. (Given:
Plancks constant h = 6.63 x 10-34 Js
and mass of electron m = 9.11 x 10-31
kg)​

Answer 1

Answer:

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Answer 2

Answer:

The lowest energy of an electron confined to move in a one-dimensional box of length 6 Å is 1.06 eV

Explanation:

The Energy of an electron in the one-dimensional box is given as      

$E_{n} = \frac{n^{2}h^{2} }{8mL^{2} }$

where L - length of the box      

    m- mass of electron      

     n- energy level

Given : L = 6 Angstrom = 6 × 10¹⁰ m

For lowest energy n= 1          

$E_{n} =\frac{1^{2}\times h^{2}} {8mL^{2} }\\E_{n} =\frac{(6.63 \times 10^{-34}) ^{2}} {8\times 9.11 \times 10^{-31} \times (6 \times 10^{-10} )^{2} }\\E_{n} =\frac{(43.956 \times 10^{-68}) } {2623.68 \times 10^{-31} \times 10^{-20} }\\E_{n} =0.017 \times 10 ^{-17}\\E_{n} =1.7 \times 10^{-19} \\\\E_{n} = 1.06$