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De-Broglie hypothesized that material particles have wave like properties. Figure shows a small particle in a box. The particle simply bounces back and forth at constant speed. As particles also have wave like properties it can be considered to be a wave reflecting back and forth from the ends of the box. The reflections will create a standing wave analogous to standing wave on a string tied at both ends. Since a standing wave confined to a region can have only selected wavelength, momentum of the particle is quantized. We can safely assume that such a particle only has kinetic energy. This energy must also be quantized. What is momentum of particle in n^(th) mode of standing wave ?A. `(nh)/(2L)`B. `(nh)/L`C. `(2nh)/L`D. `(2Ln)/h` |
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Answer» Correct Answer - A `1/lambda=RZ^(2)(1/n^(2)-1/m^(2))` for H visible is form `2rightarrow3,4,5,6`………. here`z=2` `Rightarrow 1/lambda=R(Z^(2)/n^(2)-Z^(2)/m^(2))=R(4/4^(2)-4/m^(2))4/m^(2)=1/6^(2)` `m=6 to 4,7 to 4`,……. |
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