A stationary hydrogen atom undergoes a transi | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The energy of the emitted photon during the transition from $n_2=5$ to $n_1=4$ is given by $\Delta E = h 
u = R h c \left( \frac{1}{n_1^2} - \fra

Vedclass · Accepted Answer

$\frac{9 R h}{400 m}$

Vedclass · Answer

(C) The energy of the emitted photon during the transition from $n_2=5$ to $n_1=4$ is given by $\Delta E = h 
u = R h c \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} ight)$.Since the momentum of the photon is $p = \frac{E}{c} = \frac{h}{\lambda} = R h \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} ight)$,we substitute $n_1=4$ and $n_2=5$.$p = R h \left( \frac{1}{16} - \frac{1}{25} ight) = R h \left( \frac{25-16}{400} ight) = \frac{9 R h}{400}$.By the law of conservation of linear momentum,the recoil momentum of the atom must be equal in magnitude to the momentum of the emitted photon.Therefore,$m v = p$,where $v$ is the recoil speed.$v = \frac{p}{m} = \frac{9 R h}{400 m}$.

$A$ stationary hydrogen atom undergoes a transition from $n=5$ to $n=4$. The recoil speed of the atom is (where $R=$ Rydberg constant,$h=$ Planck's constant,and $m=$ mass of the hydrogen atom).

Similar Questions

At which excited state of $Be^{3+}$ will the radius of the $e^{-}$ be the same as that of an $H$ atom in the ground state?

In the Bohr model of the hydrogen atom,the force on the electron is proportional to which power of the principal quantum number $n$?

In a hydrogen atom,an electron makes a transition from the $5^{\text{th}}$ orbit to the $3^{\text{rd}}$ orbit. The change in the angular momentum for this electron is . . . . . . .

Explain Bohr's atomic model.

The de-Broglie wavelength of an electron in the $n^{th}$ Bohr orbit is $\lambda_n$ and the angular momentum is $J_n$,then:

Vedclass Test Series

Exam Paper Generator

Online Exam Module