JEE (Advanced) 2019 Paper-2 Question 8

Question 8

A free hydrogen atom after absorbing a photon of wavelength $$\lambda_a$$ gets excited from the state n = 1 to the state n = 4. Immediately after that the electron jumps to n = m state by emitting a photon of wavelength $$\lambda_e$$. Let the change in momentum of atom due to the absorption and the emission are $$\triangle p_a$$ and $$\triangle p_e,$$ respectively. If $$\frac{\lambda_a}{\lambda_e} = \frac{1}{5}$$ which of the option(s) is/are correct?
[Use hc = 1242 eV nm ; 1 nm = $$10^{-9}$$ m, h and c are Planck’s constant and speed of light, respectively]

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