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}] $
