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
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
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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.
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.
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