Question

What is the length of a one-dimensional box for an electron (9.109 x 10-31 kg) with an n=1 energy of 479 kJ/mol? Give the answer in angstroms (A).

Answer 1

Answer : The length of a one-dimensional box for an electron is $2.819\times 10^{31}\AA$

Explanation :

The energy level of quantum particle in a one-dimensional box is given as:

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

where,

$E_n$ = 479 kJ/mol = 479000 J/mol

n = energy level = 1

h = Planck's constant = $6.626\times 10^{-34}Js$

m = mass of electron = $9.109\times 10^{-31}kg$

L = length of a one-dimensional box = ?

Now put all the given values in the above formula, we get:

$479000J/mol=\frac{(1)^2\times (6.626\times 10^{-34}Js)^2}{8\times (9.109\times 10^{-31}kg)\times L^2}$

$L=2.819\times 10^{21}m$

conversion used : $1m=10^{10}\AA$

$L=2.819\times 10^{31}\AA$

Therefore, the length of a one-dimensional box for an electron is $2.819\times 10^{31}\AA$