A proton of wavelength \(\lambda_o\) is emitted when an electron in an atom makes a transition from a level of energy 2E. If the electron transits from \(\frac{4}{3}E_k\) to E level, determine the wavelength of the photon that would be emitted
-
3\(\lambda_o\)
- 2\(\lambda_o\)
- \(\frac{3}{4}\)\(\lambda_o\)
- \(\frac{1}{3}\)\(\lambda_o\)
The correct answer is: A
Explanation
2E - E = \(\frac{hc}{\lambda}\) = E = \(\frac{hc}{\lambda}\)
\(\frac{4}{3}\)E = \(\frac{hc}{\lambda_{new}}\)
E = \(\frac{3hc}{\lambda_2}\)
\(\frac{3hc}{\lambda_2}\) = \(\frac{hc}{\lambda}\)
\(\lambda_{new}\) = 3 \(\lambda_o\)