An electron from various excited states of hydrogen atom emit radiation

Question:

An electron from various excited states of hydrogen atom emit radiation to come to the ground state. Let $\lambda_{\mathrm{n}}, \lambda_{\mathrm{g}}$ be the de Broglie wavelength of the electron in the $\mathrm{n}^{\text {th }}$ state and the ground state respectively. Let $\Lambda_{n}$ be the wavelength of the emitted photon in the transition from the $n^{\text {th }}$ state to the ground state. For large $n,(A, B$ are constants)

  1. $\Lambda_{n} \approx \mathrm{A}+\mathrm{B} \lambda_{\mathrm{n}}$

  2. $\Lambda_{\mathrm{n}}^{2} \approx \mathrm{A}+\mathrm{B} \lambda_{\mathrm{n}}^{2}$

  3. $\Lambda_{\mathrm{n}}^{2} \approx \lambda$

  4. $\Lambda_{n} \approx \mathrm{A}+\frac{\mathrm{B}}{\lambda_{\mathrm{n}}^{2}}$


Correct Option: , 4

Solution:

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