JEE Mains · Physics · STD 12 - 12. atoms
Hydrogen atom from excited state comes to the ground by emitting a photon of wavelength \(\lambda\). The value of principal quantum number ' \(n\) ' of the excited state will be: (\(R\): Rydberg constant)
- A \(\sqrt{\frac{\lambda R}{\lambda-1}}\)
- B \(\sqrt{\frac{\lambda R}{\lambda R-1}}\)
- C \(\sqrt{\frac{\lambda}{\lambda R-1}}\)
- D \(\sqrt{\frac{\lambda R^{2}}{\lambda R-1}}\)
Answer & Solution
Correct Answer
(B) \(\sqrt{\frac{\lambda R}{\lambda R-1}}\)
Step-by-step Solution
Detailed explanation
\(\frac{- Rch }{( n )^{2}}+\frac{ Rch }{1}=\frac{ hc }{\lambda}\) \(\frac{- R }{ n ^{2}}+ R =\frac{1}{\lambda}\) \(R -\frac{1}{\lambda}=\frac{ R }{ n ^{2}}\) \(\frac{\lambda R -1}{\lambda}=\frac{ R }{ n ^{2}}\)…
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
- An asteroid is moving directly towards the centre of the earth. When at a distance of \(10 \mathrm{R}\) (\(R\) is the radius of the earth) from the earths centre, it has a speed of \(12 \;\mathrm{km} / \mathrm{s}\). Neglecting the effect of earths atmosphere, what will be the speed of the asteroid when it hits the surface of the earth (escape velocity from the earth is \(11.2 \;\mathrm{km} / \mathrm{s}\) ) \(?\) Give your answer to the nearest integer in \(km/s\)JEE Mains 2020 Hard
- In a compound microscope, the magnified virtual image is formed at a distance of \(25\, cm\) from the eye-piece. The focal length of its objective lens is \(1\, cm .\) If the magnification is \(100\) and the tube length of the microscope is \(20\, cm ,\) then the focal length of the eye-piece lens (in \(cm\) ) isJEE Mains 2020 Hard
- Voltage rating of a parallel plate capacitor is \(500\,V\). Its dielectric can withstand a maximum electric field of \({10^6}\,\frac{V}{m}\). The plate area is \(10^{-4}\, m^2\) . What is the dielectric constant if the capacitance is \(15\, pF\) ? (given \({ \in _0} = 8.86 \times {10^{ - 12}}\,{C^2}\,/N{m^2}\))JEE Mains 2019 Hard
- When the temperature of a metal wire is increased from \(0^{\circ} \,C\) to \(10^{\circ}\, C\), its length increases by \(0.02 \% .\) The percentage change in its mass density will be closest to:JEE Mains 2020 Hard
- Escape velocity of a body from earth is \(11.2 \mathrm{~km} / \mathrm{s}\). If the radius of a planet be one-third the radius of earth and mass be one-sixth that of earth, the escape velocity from the plate is _______.JEE Mains 2024 Hard
- A satellite of \(10^3 \mathrm{~kg}\) mass is revolving in circular orbit of radius \(2 \mathrm{R}\). If \(\frac{10^4 \mathrm{R}}{6} \mathrm{~J}\) energy is supplied to the satellite, it would revolve in a new circular orbit of radius _______.
(use \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2, \mathrm{R}=\) radius of earth)JEE Mains 2024 Hard
More PYQs from JEE Mains
- A solid metal cube of edge length \(2\, cm\) is moving in a positive \(y-\) direction at a constant speed of \(6\, m/s\). There is a uniform magnetic field of \(0.1\, T\) in the positive \(z-\) direction. The potential difference between the two faces of the cube perpendicular to the \(x-\) axis, is.....\(mV\)JEE Mains 2019 Medium
- The ratio of 10.Powers of two motors is \(\frac{3 \sqrt{x}}{\sqrt{x}+1}\), that are capable of raising \(300\,kg\) water in \(5\) minutes and \(50\,kg\) water in \(2\) minutes respectively from a well of \(100\,m\) deep. The value of \(x\) will beJEE Mains 2023 Medium
- The angle of elevation of the top of a vertical tower from a point \(A\), due east of it is \(45^o\) . The angle of elevation of the top of the same tower from a point \(B\). due south of \(A\) is \(30^o\). If the distance between \(A\) and \(B\) is \(54\sqrt 2 \,m\), then the height of the tower (in metres), isJEE Mains 2016 Hard
- Consider the three planes \(P_{1}: 3 x+15 y+21 z=9\) ; \(P _{2}: x -3 y - z =5,\) and ; \(P_{3}: 2 x+10 y+14 z=5\). Then, which one of the following is true ?JEE Mains 2021 Medium
- A ball will a speed of \(9\, m / s\) collides with another identical ball at rest. After the collision, the direction of each ball makes an angle of \(30^{\circ}\) with the original direction. The ratio of velocities of the balls after collision is \(x : y\) where \(x\) is........JEE Mains 2021 Hard
- If \((\sqrt{3}+\mathrm{i})^{100}=2^{99}(\mathrm{p}+\mathrm{i} \mathrm{q})\), then \(\mathrm{p}\) and \(\mathrm{q}\) are roots of the equation :JEE Mains 2021 Hard