Physics And Measurement Question 190

Question: If $ m,e,{\varepsilon _{0}}, $ h and c denote mass electron, charge of electron. Planck’s constant and speed of light, respectively. The dimensions of $ \frac{me _{{}}^{4}}{\varepsilon _{0}^{2}h _{{}}^{3}c} $ are

Options:

A) [ $ M _{{}}^{0}L _{{}}^{0}T _{{}}^{-1} $ ]

B) [ $ M _{{}}^{0}L _{{}}^{-1}T _{{}}^{-1} $ ]

C) [ $ M _{{}}^{2}L _{{}}^{{}}T _{{}}^{-3} $ ]

D) [ $ M _{{}}^{0}L _{{}}^{-1}T _{{}}^{0} $ ]

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Answer:

Correct Answer: D

Solution:

[d] In Bohr’s model, $ \frac{1}{\lambda }=\frac{me^{4}}{{\varepsilon _{0}}^{2}h^{3}c}( \frac{1}{n _{1}^{2}}-\frac{1}{n _{2}^{2}} ) $

Where $ \lambda $ =wavelength, $ n _{1} $

and $ n _{2} $ are principal quantum numbers.

$ \therefore [ \frac{me^{4}}{{\varepsilon _{0}}^{2}h^{3}c} ]=[{{L}^{-1}}]=[M^{0}{{L}^{-1}}T^{0}] $



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