When a hydrogen atom,initially at rest,emits | vedclass

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(C) Given:Initial state $n_2 = 5$,final state $n_1 = 1$.Mass of hydrogen atom $m \approx 1.67 	imes 10^{-27} \, kg$.Rydberg constant $R = 1.097 	ime

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$4.3 \, m/s$

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(C) Given:Initial state $n_2 = 5$,final state $n_1 = 1$.Mass of hydrogen atom $m \approx 1.67 	imes 10^{-27} \, kg$.Rydberg constant $R = 1.097 	imes 10^7 \, m^{-1}$.Planck's constant $h = 6.63 	imes 10^{-34} \, J \cdot s$.Using the Rydberg formula for the wavelength $\lambda$ of the emitted photon:$\frac{1}{\lambda} = R \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} ight) = 1.097 	imes 10^7 \left( \frac{1}{1^2} - \frac{1}{5^2} ight) = 1.097 	imes 10^7 \left( 1 - 0.04 ight) = 1.053 	imes 10^7 \, m^{-1}$.$\lambda = \frac{1}{1.053 	imes 10^7} \approx 9.496 	imes 10^{-8} \, m$.By conservation of momentum,the momentum of the atom $p_{atom}$ must equal the momentum of the photon $p_{photon} = \frac{h}{\lambda}$.$m v = \frac{h}{\lambda} \implies v = \frac{h}{m \lambda}$.$v = \frac{6.63 	imes 10^{-34}}{(1.67 	imes 10^{-27}) 	imes (9.496 	imes 10^{-8})} \approx \frac{6.63 	imes 10^{-34}}{1.586 	imes 10^{-34}} \approx 4.18 \, m/s$.Rounding to the nearest provided option,the recoil speed is approximately $4.3 \, m/s$.

When a hydrogen atom,initially at rest,emits a photon resulting in a transition $n = 5 \rightarrow n = 1$,its recoil speed is about

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