JEE Mains · Physics · STD 12 - Atoms
- JEE Mains 2023
- Medium
- Numerical
A light of energy \(12.75 \;eV\) is incident on a hydrogen atom in its ground state. The atom absorbs the radiation and reaches to one of its excited states. The angular momentum of the atom in the excited state is \(\frac{x}{\pi} \times 10^{-17} \;eVs\). The value of \(x\) is \(........\) (use \(h=4.14 \times 10^{-15} \;eVs , c=3 \times 10^8\;\left.ms ^{-1}\right)\)
Pick an option to check your answer.
Answer & Solution
Correct Answer
(B) \(828\)
Step-by-step Solution
Detailed explanation
In the ground state energy \(=-13.6\,eV\)
So energy
\(\quad \frac{-13.6 eV }{n^2}=-13.6+12.75\)
\(\frac{-13.6 eV }{n^2}=-0.85\)
\(\quad n=\sqrt{16}\)
\(\qquad n=4\)
\(\text { Angular momentum }=\frac{n h}{2 \pi}=\frac{4 h}{2 \pi}=\frac{2 h}{\pi}\)
\(\text { Angular momentum }=\frac{2}{\pi} \times 4.14 \times 10^{-15}\)
\(\qquad=\frac{828 \times 10^{-17}}{\pi} eVs\)
More questions from Physics
- In a uniform magnetic field, the magnetic needle has a magnetic moment \(9.85 \times 10^{-2} \,{A} / {m}^{2}\) and moment of inertia \(5 \times 10^{-6} \,{kgm}^{2}\). If it performs \(10\) complete oscillations in \(5\, seconds\) then the magnitude of the magnetic field is \(....\,mT.\) [ Take \(\pi^{2}\) as \(9.85\) ]JEE Mains 2021 Medium
- In a metre-bridge when a resistance in the left gap is \(2\ \Omega\) and unknown resistance in the right gap, the balance length is found to be \(40\ \mathrm{cm}\). On shunting the unknown resistance with \(2\ \Omega\), the balance length changes by _______.JEE Mains 2024 Hard
- The electric field in an electromagnetic wave is given by \(E =56.5 \sin \omega( t - x / c ) \;NC ^{-1}\). Find the intensity of the wave if it is propagating along \(x-\)axis in the free space. (Given \(\left.\varepsilon_{0}=8.85 \times 10^{-12} \;C ^{2} N ^{-1} m ^{-2}\right)\)JEE Mains 2022 Medium
- The relation between time ' \(t\) ' and distance ' \(x\) ' is \(t=\) \(\alpha x^2+\beta x\), where \(\alpha\) and \(\beta\) are constants. The relation between acceleration \((a)\) and velocity \((v)\) is _______.JEE Mains 2024 Hard
- Consider the nuclear fission \(Ne^{20} \to 2He^4 + C^{12}\) .Given that the binding energy / nucleon of \(Ne^{20}, He^4\) and \(C^{12}\) are, respectively, \(8.03\, MeV\), \(7.07\, MeV\), and \(7.86\, MeV\), identify the correct statementJEE Mains 2019 Medium
- If sunlight is focused on a paper using convex lens, it starts burning the paper in shortest time when the lens is kept at \(30\) cm above the paper. If the radius of curvature of the lens is \(60\) cm then the refractive index of the lens material is \(\dfrac{\alpha}{10}\). The value of \(\alpha\) is _______.JEE Mains 2026 Medium
More PYQs from JEE Mains
- An alternating voltage of amplitude \(40 \mathrm{~V}\) and frequency \(4 \mathrm{kHz}\) is applied directly across the capacitor of \(12 \mu \mathrm{F}\). The maximum displacement current between the plates of the capacitor is nearly _______.JEE Mains 2024 Hard
- A current of \(2\,A\) flows through a wire of crosssectional area \(25.0\,mm ^2\). The number of free electrons in a cubic meter are \(2.0 \times 10^{28}\). The drift velocity of the electrons is \(...............\times 10^{-6}\,ms ^{-1}\) (given, charge on electron \(=1.6 \times 10^{-19}\,C\) )JEE Mains 2023 Easy
- A monoatomic gas at pressure \(P\) and volume \(V\) is suddenly compressed to one eighth of its original volume. The final pressure at constant entropy will be \(.....P\)JEE Mains 2022 Hard
- In a vernier callipers, each \(cm\) on the main scale is divided into \(20\) equal parts. If tenth vernier scale division coincides with nineth main scale division. Then the value of vernier constant will be \(\dots \; \times 10^{-2} \;mm\)JEE Mains 2022 Medium