A free electron of 2.6 , eV energy collides w | vedclass

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

Question

(C) The total energy of the system before collision is the kinetic energy of the free electron,as the potential energy at a large distance is $0$. Tot

Vedclass · Accepted Answer

$1.45 	imes 10^{9} \, MHz$

Vedclass · Answer

(C) The total energy of the system before collision is the kinetic energy of the free electron,as the potential energy at a large distance is $0$. Total energy $E_i = 2.6 \, eV + 0 = 2.6 \, eV$.The hydrogen atom is formed in the first excited state $(n=2)$. The energy of the hydrogen atom in the $n$-th state is given by $E_n = -13.6/n^2 \, eV$. For $n=2$,$E_f = -13.6/4 = -3.4 \, eV$.The energy released as a photon is the difference between the initial and final total energy: $\Delta E = E_i - E_f = 2.6 - (-3.4) = 6.0 \, eV$.Convert the energy to Joules: $\Delta E = 6.0 	imes 1.6 	imes 10^{-19} \, J = 9.6 	imes 10^{-19} \, J$.Using the relation $\Delta E = hf$,the frequency $f = \Delta E / h = (9.6 	imes 10^{-19}) / (6.6 	imes 10^{-34}) \approx 1.45 	imes 10^{15} \, Hz$.Since $1 \, MHz = 10^6 \, Hz$,the frequency in $MHz$ is $1.45 	imes 10^{15} / 10^6 = 1.45 	imes 10^9 \, MHz$.

$A$ free electron of $2.6 \, eV$ energy collides with a $H^+$ ion. This results in the formation of a hydrogen atom in the first excited state and a photon is released. Find the frequency of the emitted photon. $(h = 6.6 \times 10^{-34} \, J \cdot s)$

Similar Questions

Energy of an electron in $n^{th}$ orbit of hydrogen atom is $\left( {k = \frac{1}{{4\pi {\varepsilon _0}}}} \right)$

If $13.6 \ eV$ energy is required to ionize the hydrogen atom,then the energy required to remove an electron from $n=2$ is (in $eV$)

The recoil speed of a hydrogen atom after it emits a photon in going from $n = 5$ state to $n = 1$ state will be ..... $m/s$.

The energy levels of an electron in an atom are shown. Which transition of the electron represents the emission of a photon with the highest energy?

Vedclass Test Series

Exam Paper Generator

Online Exam Module