Answer is E= 24.092eV.
Explanation: This numerical is based on the Particle in 1-D box.
For a particle in 1-D box the energy is calculated by
[tex]E_n=\frac{n^2h^2}{8mL^2}[/tex]
where [tex]E_n[/tex] = allowed energies for a particle in a box
n = energy level
h = plank's constant
m = mass of a particle
L = length of a box
In this question, it is given the number of nodes from which we can calculate the value of "n"
Relationship between the number of nodes and the energy level is
[tex]l=n-1[/tex]
l = number of angular nodes
Number of nodes given in the question is 1, so the energy level can be calculated from the above relation.
[tex]1=n-1\\n=2[/tex]
Now, putting all the values in energy formula,
[tex]L=100\times10^-^1^2m[/tex]
Mass of electron = [tex]9.11\times10^-^3^1kg[/tex]
n = 2
h = [tex]6.63\times10^-^3^4Js[/tex]
[tex]E_2=\frac{(2)^2(6.63\times10^-^3^4Js)^2}{8(9.11\times10^-^3^1kg)(100\times10^-^1^2m)^2}\\E_2= (2)^2 (9.65\times10^-^1^9J)[/tex]
Converting Joules to eV
[tex]1J=6.242\times10^1^8eV[/tex]
[tex]E_2= (2)^2(6.023eV)\\E_2=24.092eV[/tex]
