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Q. No.
Energy and radius of the first Bohr orbit of \(He^+\) and \(Li^{2+}\) are :
[Given \(\left.\mathrm{R}_{\mathrm{H}}=2.18 \times 10^{-18} \mathrm{~J}, \mathrm{a}_0=52.9 \mathrm{pm}\right]\)
1. \(\begin{aligned} & \mathrm{E}_{\mathrm{n}}\left(\mathrm{Li}^{2+}\right)=-19.62 \times 10^{-16} \mathrm{~J} ; \\ & \mathrm{r}_{\mathrm{n}}\left(\mathrm{Li}^{2+}\right)=17.6\mathrm{pm} \\ & \mathrm{E}_{\mathrm{n}}\left(\mathrm{He}^{+}\right)=8.72 \times 10^{-16} \mathrm{~J} ; \\ & \mathrm{r}_{\mathrm{n}}\left(\mathrm{He}^{+}\right)=26.4 \mathrm{pm} \end{aligned}\)
2. \(\begin{aligned} & \mathrm{E}_{\mathrm{n}}\left(\mathrm{Li}^{2+}\right)=-8.72 \times 10^{-16} \mathrm{~J} ; \\ & \mathrm{r}_{\mathrm{n}}\left(\mathrm{Li}^{2+}\right)=17.6 \mathrm{pm} \\ & \mathrm{E}_{\mathrm{n}}\left(\mathrm{He}^{+}\right)=-19.62 \times 10^{-16} \mathrm{~J} ; \\ & \mathrm{r}_{\mathrm{n}}\left(\mathrm{He}^{+}\right)=17.6 \mathrm{pm} \end{aligned}\)
3. \(\begin{aligned} & \mathrm{E}_{\mathrm{n}}\left(\mathrm{Li}^{2+}\right)=- 19.62 \times 10^{-18} \mathrm{~J} \\ & \mathrm{r}_{\mathrm{n}}\left(\mathrm{Li}^{2+}\right)=17.6 \mathrm{pm} \\ & \mathrm{E}_{\mathrm{n}}\left(\mathrm{He}^{+}\right)=-8.72 \times 10^{-18} \mathrm{~J} \\ & \mathrm{r}_{\mathrm{n}}\left(\mathrm{He}^{+}\right)=26.4 \mathrm{pm} \end{aligned}\)
4. \(\begin{aligned} & \mathrm{E}_{\mathrm{n}}\left(\mathrm{Li}^{2+}\right)=-8.72 \times 10^{-18} \mathrm{~J} \\ & \mathrm{r}_{\mathrm{n}}\left(\mathrm{Li}^{2+}\right)=26.4 \mathrm{pm} \\ & \mathrm{E}_{\mathrm{n}}\left(\mathrm{He}^{+}\right)=-19.62 \times 10^{-18} \mathrm{~J} ; \\ & \mathrm{r}_{\mathrm{n}}\left(\mathrm{He}^{+}\right)=17.6 \mathrm{pm} \end{aligned} \)
Subtopic:  Bohr's Theory |
 67%
Level 2: 60%+
NEET - 2025
Please attempt this question first.
Hints
Please attempt this question first.
The energy of electron in the ground state \((\text{n}=1)\) for \(\text{He}^+\) ion is \(\text{-x}J,\) then that for an electron in \(\text{n}=2\) state for \(\text{Be}^{3+}\) ion in \(\text{J}\) is :
1. \(-\dfrac x9\) 2. \(-4x\)
3. \(-\dfrac 49x\) 4. \(-x\)
Subtopic:  Bohr's Theory |
 65%
Level 2: 60%+
NEET - 2024
Hints
Given below are two statements:
Statement I: The energy of the \(\mathrm{He}^{+}\) ion in \(n=2\) state is same as the energy of H atom in \(n=1\) state.
Statement II: It is possible to determine simultaneously the exact position and exact momentum of an electron in \(\mathrm{H}\) atom.
 
1. Both Statement I and Statement II are true
2. Both Statement I and Statement II are false
3. Statement I is true and Statement II is false
4. Statement I is false, and Statement II is true
Subtopic:  Bohr's Theory | Heisenberg Uncertainty Principle |
 66%
Level 2: 60%+
NEET - 2024
Hints
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Given below are two statements:
Statement I:  The Balmer spectral line for H atom with lowest energy  appears at \(\dfrac 5{36}\mathrm{ R_H~ cm^{-1}}\) (\(\mathrm{R_H}\) = Rydberg constant) 
Statement II:  When the temperature of a black body increases, the maxima of the curve (intensity versus wavelength) shifts towards shorter wavelength.
In the light of the above statements, choose the correct answer from the options given below:
 
1. Statement I is correct and Statement II is incorrect.
2. Statement I is incorrect and Statement II is correct.
3. Both Statement I and Statement II are correct.
4. Both Statement I and Statement II are incorrect.
Subtopic:  Bohr's Theory | Planck's Theory |
 67%
Level 2: 60%+
NEET - 2024
Hints

Based on equation E = –2.178 × 10–18J, Z2n2 certain conclusions are written. Which of them is not correct?

1. Larger the value of n, the larger the orbit radius.
2. Equation can be used to calculate the change in energy when the electron changes orbit.
3. For n = 1, the electron has a more negative energy than it does for n = 6 which means that the electron is more loosely bound in the smallest allowed orbit.
4. The negative sign in the equation simply means that the energy of the electron bound to the nucleus is lower than what it would be if the electrons were at an infinite distance from the nucleus.
Subtopic:  Bohr's Theory |
 67%
Level 2: 60%+
AIPMT - 2013
Hints
The total number of atomic orbitals in fourth energy level of an atom is:

1.  16
2.  32
3.  4
4.  8

Subtopic:  Bohr's Theory |
 77%
Level 2: 60%+
AIPMT - 2011
Hints
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The energies E1 and E2 of two radiations are 25 eV and 50 eV respectively. The relation between their wavelengths i.e., λ1 and λ2 will be:

1.  λ1=2λ2

2.  λ1=4λ2

3.  λ1=12λ2

4.  λ1=λ2

Subtopic:  Bohr's Theory |
 86%
Level 1: 80%+
AIPMT - 2011
Hints

If the energy of the second Bohr orbit of the hydrogen atom is –328 kJ mol–1, the energy of the fourth Bohr orbit would be:

1. –1312 kJ mol–1 2. –82 kJ mol–1
3. –41 kJ mol–1 4. –164 kJ mol–1
Subtopic:  Bohr's Theory |
 76%
Level 2: 60%+
AIPMT - 2005
Hints

The ionization energy required to remove an electron from the second orbit of \(\text{Li}^{2+}\) is:
1.  122.4 eV
2.  40.8 eV
3.  30.6 eV
4.  13.6 eV

Subtopic:  Bohr's Theory |
 71%
Level 2: 60%+
AIPMT - 1999
Hints
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The radius of a hydrogen shell is 0.53Å. In its first excited state, radius of the shell will be:
1. 2.12 Å
2. 1.06 Å
3. 8.5 Å
4. 4.24 Å

Subtopic:  Bohr's Theory |
 81%
Level 1: 80%+
AIPMT - 1998
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