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A photon with wavelength 11. 0 nm is absorbed when an electron in a three-dimensional cubical box makes a transition from the ground state to the second excited state

Sagot :

For a photon with wavelength 11. 0 nm,  the side length LL of the box is mathematically given as

L=1.414*10^{-27}m

What is the side length LL of the box?

Generally, the equation for the change in energy is mathematically given as

[tex]dE=\frac{hc}{\lambda}[/tex]

Therefore

[tex]\frac{hc}{\lambda}=\frac{6h^2}{8ml}\\\\L=\sqrt{6h\lambda}{8mc}\\\\L=\sqrt{\frac{6(6.626*10^{-34})*11.0*10^{-9}}{8(9.11*10^31)(3*10^8)}}[/tex]

L=1.414*10^{-27}m

In conclusion,  the side length LL of the box is

L=1.414*10^{-27}m

Read more about Mesurement

https://brainly.com/question/17972372

The side length of the box for a photon of wavelength 11. 0 nm will be [tex]\rm L = 1.414 \times 10^{-27}[/tex] m.

What is wavelength?

The distance between two successive troughs or crests is known as the wavelength. The peak of the wave is the highest point, while the trough is the lowest.

The change in the energy of the photon is found as;

[tex]\rm dE = \frac{hc}{\lambda} \\\\ \frac{hc}{\lambda} =\frac{6h^2}{8ml} \\\\ L= \sqrt{\frac{6h\lambda}{8mc} } \\\\ L = \sqrt{\frac{6 \times 6.626 \times 10^{-34}\times 11 \times 10^{-9}}{8 \times 9.11 \times 10^{31} \times 3 \times10^8} } \\\\ L= 1.414 \times 10^{-27} \ m[/tex]

Hence  the side length of the box for a photon of wavelength 11. 0 nm will be [tex]\rm L = 1.414 \times 10^{-27}[/tex] m.

To learn more about the wavelength refer to the link;

brainly.com/question/7143261

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