MHT CET · Physics · Atomic Physics
The potential energy of the orbital electron in the ground state of hydrogen atoms is \(-\mathrm{E}\). What is the kinetic energy?
- A \(4 \mathrm{E}\)
- B \(\frac{E}{4}\)
- C \(\frac{E}{2}\)
- D \(2 E\)
Answer & Solution
Correct Answer
(C) \(\frac{E}{2}\)
Step-by-step Solution
Detailed explanation
The potential energy of
\(\mathrm{U}(\mathrm{n}=1)=-\mathrm{E}\)
Goomd state: total energy is given by
\(\mathrm{TE}=\mathrm{U}+\mathrm{K}\)
\(\mathrm{U}=-\frac{\left(\mathrm{ze}^2\right)}{4 \pi \varepsilon_0}\)
For orbit consider force balance
\(\frac{\mathrm{ze}^2}{4 \pi \varepsilon_0 \mathrm{r}^2}=\frac{\mathrm{mv}^2}{\mathrm{r}}\)
\(\therefore \mathrm{K}=\frac{\mathrm{mv}^2}{2}=\frac{1}{2}\left(\frac{\mathrm{ze}^2}{4 \pi \varepsilon_0 \mathrm{r}^2}\right)\)
Thus, \(\mathrm{K}=\frac{\mathrm{E}}{2}=\frac{\mathrm{U}}{2}\)
\(\mathrm{U}(\mathrm{n}=1)=-\mathrm{E}\)
Goomd state: total energy is given by
\(\mathrm{TE}=\mathrm{U}+\mathrm{K}\)
\(\mathrm{U}=-\frac{\left(\mathrm{ze}^2\right)}{4 \pi \varepsilon_0}\)
For orbit consider force balance
\(\frac{\mathrm{ze}^2}{4 \pi \varepsilon_0 \mathrm{r}^2}=\frac{\mathrm{mv}^2}{\mathrm{r}}\)
\(\therefore \mathrm{K}=\frac{\mathrm{mv}^2}{2}=\frac{1}{2}\left(\frac{\mathrm{ze}^2}{4 \pi \varepsilon_0 \mathrm{r}^2}\right)\)
Thus, \(\mathrm{K}=\frac{\mathrm{E}}{2}=\frac{\mathrm{U}}{2}\)
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
- A thin uniform rod of length ' \(L\) ' and mass ' \(M\) ', is swinging freely along a horizontal axis passing through its centre. Its maximum angular speed is ' \(\omega\) '. Its centre of mass rises to a maximum height of [g= gravitational acceleration]MHT CET 2024 Hard
- A meter scale is supported on a wedge at its centre of gravity. A body of weight ' \(w\) ' is suspended from the 20 cm mark and another weight of 25 gram is suspended from 74 cm mark balances it and the meter scale remains perfectly horizontal. Neglecting the weight of the meter scale, the weight of the body isMHT CET 2024 Easy
- Two bodies rotate with kinetic energies ' \(E_1\) ' and ' \(E_2\) '. Moment of inertia about their axis of rotation are ' \(I_1\) ' and ' \(I_2\) '. If \(I_1=\frac{I_2}{3}\) and \(\mathrm{E}_1=27 \mathrm{E}_2\), then the ratio of angular momenta ' \(\mathrm{L}_1\) ' to ' \(\mathrm{L}_2\) ' isMHT CET 2021 Medium
- Acceleration of an electron in the first Bohr's orbit is proportional to \(\mathrm{m}=\) mass of electron, \(\mathrm{r}=\) radius of the orbit, \(\mathrm{h}=\) Planck's constant)MHT CET 2024 Medium
- A vehicle starts from rest and accelerates along straight path at \(2 \mathrm{~m} / \mathrm{s}^2\). At the starting point of the vehicle, there is a stationary electric siren. How far has the vehicle nearly gone when the driver hears the siren at \(94 \%\) of its value when the vehicle was at rest?
(speed of sound \(=330 \mathrm{~m} / \mathrm{s}\) )MHT CET 2025 Medium - If a unit vector is represented as \(\overrightarrow{\mathrm{u}}=0 \cdot 4 \hat{\imath}+0 \cdot 7 \hat{\jmath}+\mathrm{c} \hat{k}\), then the value of ' \(\mathrm{c}\) ' isMHT CET 2020 Easy
More PYQs from MHT CET
- When a.c. source is connected across a pure capacitor, the correct phase relation between current \(\left(\mathrm{i}_{\mathrm{c}}\right)\) and voltage \(\left(\mathrm{e}_{\mathrm{c}}\right)\) is shown in figure
MHT CET 2022 Hard - Total number of minor calyces is equal to that ofMHT CET 2024 Easy
- A string of mass 0.2 Kg is under a tension of 2.5 N . The length of the string is 2 m . A transverse wave starts from one end of the string. The time taken by the wave to reach the other end isMHT CET 2024 Medium
- The area (in sq. units) bounded by the curves \(y=(x+1)^2, y=(x-1)^2\) and the line \(y=\frac{1}{4}\) isMHT CET 2024 Hard
- If the equation \(\cos ^4 \theta+\sin ^4 \theta+\lambda=0\). has real solutions for \(\theta\), then \(\lambda\) lies in the intervalMHT CET 2024 Hard
- A bundle of axons inside the central nervous system is ________.MHT CET 2025 Hard