NEET Physics Question - Modern Physics - Photoelectric Effects and deBroglie Equation

Assertion (A): The ratio of wavelength in first transition of lyman series for H atom and He+ atom is exactly equal to four.

Reason (R): In all atoms electron revolve around fixed nucleus.

Both (A) & (R) are true and the (R) is the correct explanation of the (A)

Both (A) & (R) are true but the (R) is not the correct explanation of the (A)

(A) is true but (R) is false

Both (A) and (R) are false

Solution:

The wavelength for hydrogen-like atoms is given by \(1/\lambda \propto Z^2\). For the first transition of the Lyman series (n=1 to n=2), \(lambda_H = 4/(3R)\) and \(lambda_{\text{He}^+} = 1/(3R)\). Their ratio \(lambda_H / \lambda_{\text{He}^+} = 4\). So (A) is true. Reason (R) is false as nuclei are not perfectly fixed; they exhibit recoil and vibration.

Rankers Physics

Wavelength Ratio in Lyman Series

Solution:

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