The electron energy in a hydrogen atom is given by $E_n = (-2.18 \times 10^{-18})/n^2 \ J$. Calculate the energy required to remove an electron completely from the $n = 2$ orbit. What is the longest wavelength of light in $cm$ that can be used to cause this transition?
(A) Given,$E_n = -\frac{2.18 \times 10^{-18}}{n^2} \ J$.
Energy required for ionization from $n = 2$ is $\Delta E = E_{\infty} - E_2$.
Since $E_{\infty} = 0$,$\Delta E = 0 - (\frac{-2.18 \times 10^{-18}}{2^2}) = \frac{2.18 \times 10^{-18}}{4} = 5.45 \times 10^{-19} \ J$.
Using $\lambda = \frac{hc}{\Delta E}$,where $h = 6.626 \times 10^{-34} \ J \cdot s$ and $c = 3 \times 10^8 \ m/s$:
$\lambda = \frac{(6.626 \times 10^{-34} \ J \cdot s)(3 \times 10^8 \ m/s)}{5.45 \times 10^{-19} \ J} = 3.647 \times 10^{-7} \ m$.
Converting to $cm$: $\lambda = 3.647 \times 10^{-7} \ m \times 100 \ cm/m = 3.647 \times 10^{-5} \ cm$.
Energy required for ionization from $n = 2$ is $\Delta E = E_{\infty} - E_2$.
Since $E_{\infty} = 0$,$\Delta E = 0 - (\frac{-2.18 \times 10^{-18}}{2^2}) = \frac{2.18 \times 10^{-18}}{4} = 5.45 \times 10^{-19} \ J$.
Using $\lambda = \frac{hc}{\Delta E}$,where $h = 6.626 \times 10^{-34} \ J \cdot s$ and $c = 3 \times 10^8 \ m/s$:
$\lambda = \frac{(6.626 \times 10^{-34} \ J \cdot s)(3 \times 10^8 \ m/s)}{5.45 \times 10^{-19} \ J} = 3.647 \times 10^{-7} \ m$.
Converting to $cm$: $\lambda = 3.647 \times 10^{-7} \ m \times 100 \ cm/m = 3.647 \times 10^{-5} \ cm$.
Explore More
Similar Questions
$A$ surface ejects electrons when hit by green light but not when hit by yellow light. Will electrons be ejected if the surface is hit by red light?
Medium
View SolutionThe ground state energy of a $H$ atom is given as $-13.6 \, eV$. The energy of the second excited state will be .......... $eV$.
Medium
View SolutionThe value of Rydberg constant $\left(R_H\right)$ is $2.18 \times 10^{-18} \ J$. The velocity of an electron having mass $9.1 \times 10^{-31} \ kg$ in Bohr's first orbit of a hydrogen atom $= \dots \dots \dots \times 10^5 \ ms^{-1}$ (nearest integer).
Energy levels $A, B, C$ of a certain atom correspond to increasing values of energy,$i.e.,$ $E_A < E_B < E_C$. If $\lambda_1, \lambda_2$ and $\lambda_3$ are the wavelengths of radiations corresponding to the transitions $C$ to $B$,$B$ to $A$ and $C$ to $A$ respectively,which of the following statements is correct?
Difficult
View SolutionThe radius of the first excited state of a Helium ion $(He^+)$ is given by (where $a_0$ is the radius of the first stationary state of the hydrogen atom):
Vedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo