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A certain atom requires 3.0 eV of energy to excite an electron from the ground level to the first excited level. Model the atom as an electron in a box and find the width L of the box.

Short Answer

Expert verified

The width L of the box is 6.14×10-10m.

Step by step solution

01

Define the energy level.

The energy level of a particle of massin a box of width Lis:

En=Pn22m=n2h28mL2=n2Ï€2h22mL2n=1,2,3,...

02

Determine the width of box.

Given that, energy of photon at ground level is 3.0 eV.

The energy E1in joule is

E1=3.00×1.60×10-191=4.80×10-19J

The difference in energy between levels n = 2 and n = 1 is:

∆E=E2-E1=22-12π2h22mL2=3E1=3π2h22mL2

The mass of electron is9.11×10-31kgand value ofh=1.055×10-34J⋅s.

The width of the box is:

L=3nÏ€³ó2mEn=3Ï€1.055×10-3429.11×10-314.80×10-19=6.14×10-10m

Hence, the width L of the box is 6.14×10-10m.

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