NEET · Physics · STD 12 - 12. atoms
In the first excited state of hydrogen atom, the energy of its electron is −3.4 eV. The radial distance of the electron from the hydrogen nucleus in this case is approximately :
(Take \(1 eV =1.6 \times 10^{-19} J, e=1.6 \times 10^{-19} C\) and \(\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 N m ^2 / C ^2\) )
- A \(2.1 \times 10^{-9} m\)
- B \(2.1 \times 10^{-8} m\)
- C \(2.1 \times 10^{-10} m\)
- D \(2.1 \times 10^{-11} m\)
Answer & Solution
Correct Answer
(C) \(2.1 \times 10^{-10} m\)
Step-by-step Solution
Detailed explanation
(C) \(2.1 \times 10^{-10} m\)
The total energy of an electron in a hydrogen atom is given by \(E=-\frac{1}{4 \pi \varepsilon_0} \frac{e^2}{2 r}\)
Substituting the given values:
\(-3.4 \times 1.6 \times 10^{-19}=-\frac{9 \times 10^9 \times\left(1.6 \times 10^{-19}\right)^2}{2 r}\)
\(r=\frac{9 \times 10^9 \times 1.6 \times 10^{-19}}{2 \times 3.4}\)
\(r=\frac{14.4 \times 10^{-10}}{6.8}\)
\(r \approx 2.117 \times 10^{-10} m\)
The total energy of an electron in a hydrogen atom is given by \(E=-\frac{1}{4 \pi \varepsilon_0} \frac{e^2}{2 r}\)
Substituting the given values:
\(-3.4 \times 1.6 \times 10^{-19}=-\frac{9 \times 10^9 \times\left(1.6 \times 10^{-19}\right)^2}{2 r}\)
\(r=\frac{9 \times 10^9 \times 1.6 \times 10^{-19}}{2 \times 3.4}\)
\(r=\frac{14.4 \times 10^{-10}}{6.8}\)
\(r \approx 2.117 \times 10^{-10} m\)
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 horizontal bridge is built across a river. A student standing on the bridge throws a small ball vertically upwards with a velocity \(4\,m s ^{-1}\). The ball strikes the water surface after \(4\,s\). The height of bridge above water surface is \(......\,m\) \(\left(\right.\) Take \(\left.g=10\,m s ^{-2}\right)\)NEET 2023 Medium
- The angle between \((\overrightarrow A - \overrightarrow B )\) and \((\overrightarrow A \times \overrightarrow B )\) is \((\overrightarrow{ A } \neq \overrightarrow{ B })\)NEET 2017 Easy
- The quantities of heat required to raise the temperature of two solid copper spheres of radil \(r _{1}\) and \(r _{2}\left( r _{1}=1.5 r _{2}\right)\) through \(1\;K\) are in the ratioNEET 2020 Medium
- When two monochromatic lights of frequency, \(v\) and \(\frac{v}{2}\) are incident on a photoelectric metal, their stopping potential becomes \(\frac{V_{S}}{2}\) and \(V_{s}\) respectively. The threshold frequency for this metal is :NEET 2022 Medium
- In some appropriate units, time \((t)\) and position \((x)\) relation of a moving particle is given by \(t=x^2+x\). The acceleration of the particle isNEET 2025 Hard
- Two particles of mass \(5\, kg\) and \(10\, kg\) respectively are attached to the two ends of a rigid rod of length \(1\, m\) with negligible mass. The centre of mass of the system from the \(5\, kg\) particle is nearly at a distance of \(..........\, cm\)NEET 2020 Medium
More PYQs from NEET
- The Golgi complex participates inNEET 2018 Medium
- Light with an average flux of \(20\, W / cm ^{2}\) falls on a non-reflecting surface at normal incidence having surface area \(20\, cm ^{2} .\) The energy recelved by the surface during time span of \(1\) minute is \(............J\)NEET 2020 Medium
- Match the following columns and select the correct option.
\((a)\quad(b)\quad(c)\quad(d)\)Column \(- I\) Column \(- II\) \((a)\) Clostridium butylicum \((i)\) Cyclosporin \(- A\) \((b)\) Trichoderma polysporum \((ii)\) Butyric Acid \((c)\) Monascus purpureus \((iii)\) Citric Acid \((d)\) Aspergillus niger \((iv)\) Blood cholesterol lowering agent NEET 2020 Easy - Given below are two statements:
Statement \(I\) : During G0 phase of cell cycle, the cell is metabolically inactive.
Statement \(II\) : The centrosome undergoes duplication during S phase of interphase.
In the light of the above statements, choose the most appropriate answer from the options given below:NEET 2023 Medium - A diagram showing axon terminal and synapse is given. Identify correctly at least two of \(A - D\).
NEET 2013 Medium - Match List I with List II :
Choose the option with all correct matches.List - I List - II A. Scutellum (i) Persistent nucellus B. Non-albuminous seed (ii) Cotyledon of Monocot seed C. Epiblast (iii) Groundnut D. Perisperm (iv) Rudimentary cotyledon NEET 2025 Medium