MHT CET · Physics · Atomic Physics
The ratio of longest to shortest wavelength emitted in Paschen series of hydrogen atom is
- A \(\frac{144}{63}\)
- B \(\frac{25}{9}\)
- C \(\frac{9}{25}\)
- D \(\frac{63}{144}\)
Answer & Solution
Correct Answer
(A) \(\frac{144}{63}\)
Step-by-step Solution
Detailed explanation
For Paschen series, Longest wavelength corresponds to
\(\begin{aligned}
& \mathrm{n}_1=3, \mathrm{n}_2=\mathrm{n}_1+1=4 \\
& \lambda_{\max }=\frac{144}{7 \mathrm{R}}
\end{aligned}\)
Shortest wavelength corresponds to \(\mathrm{n}_1=3, \mathrm{n}_2=\infty\)
\(\begin{aligned}
\lambda_{\min } & =\frac{9}{R} \\
\therefore \quad & \frac{\lambda_{\max }}{\lambda_{\min }}=\frac{\left(\frac{144}{7 R}\right)}{\left(\frac{9}{R}\right)}=\frac{144}{63}
\end{aligned}\)
\(\begin{aligned}
& \mathrm{n}_1=3, \mathrm{n}_2=\mathrm{n}_1+1=4 \\
& \lambda_{\max }=\frac{144}{7 \mathrm{R}}
\end{aligned}\)
Shortest wavelength corresponds to \(\mathrm{n}_1=3, \mathrm{n}_2=\infty\)
\(\begin{aligned}
\lambda_{\min } & =\frac{9}{R} \\
\therefore \quad & \frac{\lambda_{\max }}{\lambda_{\min }}=\frac{\left(\frac{144}{7 R}\right)}{\left(\frac{9}{R}\right)}=\frac{144}{63}
\end{aligned}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- Two bar magnets \(A\) and \(B\) are geometrically similar but the magnetic moment of \(A\) is twice that of \(B\). \(T_1\) is the time period of oscillation when their like poles are kept together. When unlike poles are kept together, the time period of oscillation is \(\mathrm{T}_2\). The ratio \(\mathrm{T}_1: \mathrm{T}_2\) will beMHT CET 2025 Medium
- In a photoelectric emission experiment, the stopping potential for a given metal is \(V\) volt, when radiation of wavelength \(\lambda\) is used. If radiation of wavelength \(2 \lambda\) is used with the same metal, then the stopping potential (in volt) will be
\(\text {[ } c \text { = velocity of light, } e=\text { charge on electron,}\) \( h=\text { Planck's constant }]\)MHT CET 2022 Medium - The radius of planet is twice the radius of the earth. Both have almost equal average mass densities. If ' \(V_P\) ' and ' \(V_E\) ' are escape velocities of the planet and the earth respectively, thenMHT CET 2021 Medium
- The maximum wavelength of radiation emitted by a star is 289.8 nm. Then intensity of radiation for the star is (Given : Stefan’s constant = , Wien’s constant,MHT CET 2019 Medium
- A monoatomic ideal gas is heated at constant pressure. The percentage of total heat used in changing the internal energy isMHT CET 2024 Easy
- An inductance coil has a resistance of \(100 \Omega\). When are a.c. signal of frequency \(100 \mathrm{Hzis}\) applied to the coil, the voltage leads the current by \(45^{\circ}\). The inductance of the coil in henry is \(\left[\sin 45^{\circ}=\cos 45^{\circ}=\frac{1}{\sqrt{2}}\right]\)MHT CET 2022 Easy
More PYQs from MHT CET
- Which one of the following is considered as molecular scissors in modern biotechnology?MHT CET 2025 Easy
- A closed pipe containing a liquid showed a pressure \(P_1\) by gauge. When the valve was opened, pressure was reduced to \(P_2\). The speed of water flowing out of the pipe is ( \(\rho=\) density of water )MHT CET 2024 Easy
- A solid cylinder of mass \(M\) and radius \(R\) is rotating about its geometrical axis. A solid sphere of the same mass and same radius is also rotating about its diameter with an angular speed half that of the cylinder. The ratio of the kinetic energy of rotation of the sphere to that of the cylinder will beMHT CET 2024 Medium
- Which from the following statements is correct for aqueous solution of \(6 \mathrm{gL}^{-1}\) urea and \(17 \cdot 12 \mathrm{~g} \mathrm{~L}^{-1}\) of sucrose?
[Molar mass of urea \(=60 \mathrm{~g} \mathrm{~mol}^{-1}\)
Molar mass of sucrose \(=342 \mathrm{~g} \mathrm{~mol}^{-1}\) ]MHT CET 2024 Medium - The oxidation number of \(\mathrm{C}\) atom in \(\mathrm{CH}_{2} \mathrm{Cl}_{2}\) and \(\mathrm{CCl}_{4}\) are respectivelyMHT CET 2012 Easy
- \(\lim _{x \rightarrow 0} \frac{x \tan 2 x-2 x \tan x}{(1-\cos 2 x)^2}\) isMHT CET 2024 Hard