Respuesta :
Answer:
Width of a box, [tex]l=6.41\times 10^{-15}\ m[/tex]
Explanation:
The ground level energy of a proton in a box is, E = 5 MeV
[tex]E =5\times 10^6\ eV\\\\=5\times 10^6\times 1.6\times 10^{-19}\\\\=8\times 10^{-13}\ J[/tex]
Energy in a box is given by :
[tex]E=\dfrac{n^2h^2}{8ml^2}[/tex]
For ground state, n = 1
m is mass of proton
h is Planck's constant
l is width of the box
[tex]l^2=\dfrac{n^2h^2}{8mE}\\\\l^2=\dfrac{1^2\times (6.63\times 10^{-34})^2}{8\times 1.67\times 10^{-27}\times 8\times 10^{-13}}\\\\l=\sqrt{\dfrac{1^{2}\times(6.63\times10^{-34})^{2}}{8\times1.67\times10^{-27}\times8\times10^{-13}}}\\\\l=6.41\times 10^{-15}\ m[/tex]
So, the width of the bx is [tex]6.41\times 10^{-15}\ m[/tex].
The width of the box, for the ground level energy with which the particles in a nucleus are bound, is 6.41×10⁻¹⁵ m.
What is the energy in a box?
The energy in a box can be calculated with the following formula.
[tex]E=\dfrac{n^2h^2}{8mL^2}[/tex]
Here, (E) is the energy at the nth state, (n) n is the quantum number, (h) is plank's constant and (L) is the width of the box.
The proton is in a box of width L. The width of the box be for the ground level energy to be 5.0 MeV, a typical value for the energy with which the particles in a nucleus are bound.
The energy of the box is at ground level. Then the value of nth state will be 1. It is known that the value of plank's constant is 6.63×10⁻³⁴ m²kg/s.
Put this values in the above formula as,
[tex]8\times10^{-13}=\dfrac{(1)^2(6.63\times10^{-34})^2}{8(1.67\times10^{27})(l)^2}\\l=6.41\times10^{-15}\rm\; m[/tex]
Thus, the width of the box, for the ground level energy with which the particles in a nucleus are bound, is 6.41×10⁻¹⁵ m.
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