JEE Mains · Physics · STD 12 - 12. atoms
In \(Li^{++},\) electron in first Bohr orbit is excited to a level by a radiation of wavelength \(\lambda .\) When the ion gets deexcited to the ground state in all possible ways(including intermediate emission) a total of six spectral lines are observed. What is the value of \(\lambda \)?.....\(nm\) (Given: \(h = 6.63\times 10^{34}\,js; e = 3 \times 10^8\,ms^{-1}\) )
- A \(10.8\)
- B \(11.4\)
- C \(9.4\)
- D \(12.3\)
Answer & Solution
Correct Answer
(A) \(10.8\)
Step-by-step Solution
Detailed explanation
\(\frac{h c}{\lambda}=13.6\, \mathrm{eV}(\mathrm{g})\left\{1-\frac{1}{16}\right\}\) \(\frac{1240\, \mathrm{eV}}{\lambda}=\frac{15}{16} \times 9 \times 13.6\, \mathrm{eV}\) \(\lambda=\frac{1240 \times 16}{15 \times 9 \times 13.6}=10.8\, \mathrm{nm}\)
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
- A hollow spherical shell at outer radius \(R\) floats just submerged under the water surface. The inner radius of the shell is \(r\). If the specific gravity of the shell material is \(\frac{27}{8}\) \(w.r.t.\) water, the value of \(r\) is\(......R\)JEE Mains 2020 Hard
- Two vectors \(\overrightarrow{ A }\) and \(\overrightarrow{ B }\) have equal magnitudes. If magnitude of \(\overrightarrow{ A }+\overrightarrow{ B }\) is equal to two times the magnitude of \(\overrightarrow{ A }-\overrightarrow{ B }\), then the angle between \(\overrightarrow{ A }\) and \(\overrightarrow{ B }\) will be .......................JEE Mains 2022 Medium
- A plane electromagnetic wave, has frequency of \(2.0 \times 10^{10}\, Hz\) and its energy density is \(1.02 \times 10^{-8}\, J / m ^{3}\) in vacuum. The amplitude of the magnetic field of the wave is close to\(....nT\) \(\left(\frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{\circ} \frac{ Nm ^{2}}{ C ^{2}}\right.\) and speed of \(1 ight\) \(\left.=3 \times 10^{8}\, ms ^{-1}\right)\)JEE Mains 2020 Hard
- The driver sitting inside a parked car is watching vehicles approaching from behind with the help of his side view mirror, which is a convex mirror with radius of curvature \(\mathrm{R}=2 \mathrm{~m}\). Another car approaches him from behind with a uniform speed of \(90 \mathrm{~km} / \mathrm{hr}\). When the car is at a distance of 24 m from him, the magnitude of the acceleration of the image of the car in the side view mirror is ' a '. The value of 100 a is _______ \(\mathrm{m} / \mathrm{s}^2\).JEE Mains 2025 Hard
- The workdone in an adiabatic change in an ideal gas depends upon only :JEE Mains 2025 Easy
- Two lighter nuclei combine to form a comparatively heavier nucleus by the relation given below: \({ }_{1}^{2} X +{ }_{1}^{2} X ={ }_{2}^{4} Y\) The binding energies per nucleon \({ }_{1}^{2} X\) and \({ }_{2}^{4} Y\) are \(1.1\,MeV\) and \(7.6\,MeV\) respectively. The energy released in this process is \(MeV\).JEE Mains 2022 Medium
More PYQs from JEE Mains
- In a nuclear fission process, a high mass nuclide \((A \approx 236)\) with binding energy \(7.6\ \mathrm{MeV} /\) Nucleon dissociated into middle mass nuclides \((A \approx 118)\), having binding energy of \(8.6 \ \mathrm{MeV} / \mathrm{Nucleon}\). The energy released in the process would be \(\mathrm{MeV}\).JEE Mains 2024 Hard
- When both jaws of vernier callipers touch each other, zero mark of the vernier scale is right to zero mark of main scale, \(4^{\text {th}}\) mark on vernier scale coincides with certain mark on the main scale. While measuring the length of a cylinder, observer observes 15 divisions on main scale and \(5^{\text {th}}\) division of vernier scale coincides with a main scale division. Measured length of cylinder is ___________ mm. (Least count of Vernier calliper \(= 0.1\ mm\))JEE Mains 2026 Easy
- By what percentage will the illumination of the lamp decrease if the current drops by \(20 \%\) ?JEE Mains 2024 Hard
- When one moves from a point \(16\) km below the earth's surface to a point \(16\) km above the earth's surface. The change in \(g\) is approximately \(\alpha\) %. The value of \(\alpha\) is _____.
(Take radius of the earth \(= 6400\) km.)JEE Mains 2026 Medium - \(27\) similar drops of mercury are maintained at \(10 \,V\) each. All these spherical drops combine into a single big drop. The potential energy of the bigger drop is ....... times that of a smaller drop.JEE Mains 2021 Hard
- If \(\cos \,\left( {\alpha + \beta } \right) = \frac{3}{5},\,\sin \,\left( {\alpha - \beta } \right) = \frac{5}{{13}}\) and \(0 < \alpha ,\beta < \frac{\pi }{4}\) then \(\tan \,\left( {2\alpha } \right)\) is equal toJEE Mains 2019 Hard