An electron collides with a fixed hydrogen at | vedclass

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

Question

(C) The longest wavelength of the Balmer series for a hydrogen atom corresponds to the transition of an electron from the $n=3$ state to the $n=2$ sta

Vedclass · Accepted Answer

$12.1$

Vedclass · Answer

(C) The longest wavelength of the Balmer series for a hydrogen atom corresponds to the transition of an electron from the $n=3$ state to the $n=2$ state.This implies that when the hydrogen atom was excited by the colliding electron,the electron was promoted from the $n=1$ ground state to the $n=3$ excited state.The energy of the $n$-th quantum state for a hydrogen atom is given by $E_n = -\frac{13.6}{n^2} 	ext{ eV}$.For the ground state $(n=1)$: $E_1 = -\frac{13.6}{1^2} = -13.6 	ext{ eV}$.For the excited state $(n=3)$: $E_3 = -\frac{13.6}{3^2} = -1.51 	ext{ eV}$.The energy required for this excitation is $\Delta E = E_3 - E_1 = -1.51 - (-13.6) = 12.09 	ext{ eV} \approx 12.1 	ext{ eV}$.Since the colliding electron loses all its kinetic energy to excite the atom,the minimum kinetic energy of the electron must be equal to the excitation energy,which is $12.1 	ext{ eV}$.

Similar Questions

The binding energy of an electron in the ground state of a hydrogen atom is $13.6 \ eV$. What is the energy in $eV$ required to remove an electron from the first excited state of a $Li^{++}$ ion?

Energy of a stationary electron in the hydrogen atom is $E = -\frac{13.6}{n^2} \text{ eV}$. Calculate the energies required to excite the electron in a hydrogen atom to $(a)$ its second excited state and $(b)$ its ionized state,respectively.

What is an emission line?

In the above figure,$D$ and $E$ respectively represent:

The energy of a hydrogen atom in its ground state is $-13.6 \ eV$. The energy of the level corresponding to the quantum number $n = 2$ (first excited state) in the hydrogen atom is......$eV$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module