A) \[\Lambda _{n}^{2}\approx A+B\lambda _{n}^{2}\]
B) \[\Lambda _{n}^{2}\approx \lambda \]
C) \[{{\Lambda }_{n}}\approx A+\frac{B}{\lambda _{n}^{2}}\]
D) \[{{\Lambda }_{n}}\approx A+B{{\lambda }_{n}}\]
Correct Answer: C
Solution :
| [c] De Broglie wavelength\[{{\lambda }_{n}}\] |
| \[=\frac{h}{mv}=\frac{h}{\frac{m{{e}^{2}}}{2n{{\in }_{0}}}}=(const)n\] |
| For wavelength of emitted photon |
| \[\frac{hc}{{{\Lambda }_{n}}}=13.6\left( 1-\frac{1}{{{n}^{2}}} \right)eV\] |
| \[{{\Lambda }_{n}}=\frac{hc}{13.6}{{\left( 1-\frac{1}{{{n}^{2}}} \right)}^{-1}}units\] |
| \[=\frac{hc}{13.6}\left( 1+\frac{1}{{{n}^{2}}} \right)units\] |
| \[=A+\frac{B}{{{\lambda }_{n}}^{2}}\] |
| As \[{{\lambda }_{n}}\propto n\] |
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