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An electron confined in a one-dimensional box emits a 200 nm photon in a quantum jump from n=2 to n =1. What is the length of the box?

Short Answer

Expert verified

Tthe length of the box is L=426.4pm

Step by step solution

01

Given information

An electron confined in a one-dimensional box emits a 200 nm photon in a quantum jump from n=2 to n =1.

02

Explanation

Energy levels of the particle in the box:

En=h2n28mL2

Energy of the photon:

ΔE12=hcλ

Substitute energy levels:

role="math" localid="1648514586435" E2-E1=h2·228mL2-h2·128mL2E2-E1=3h28mL2

Substitute energy of the photon:

hcλ=3h28mL2

03

Calculations:

Express the above equation in terms of L:

L=3h2λ8mhc

Substitute the values:

L=36.63·10-342·200·10-98·9.11·10-31·6.63·10-34·3·108L=426.4pm

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