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Atoms is a small chapter that JEE Main asks from almost every year, and the questions are nearly always a direct substitution into one of the Bohr relations. Where students lose marks is the Z in the formulas — the paper likes to ask about a helium ion rather than hydrogen, and the energy then jumps by a factor of four. Ten questions below. Give them ten honest minutes.
What this chapter carries in JEE Main
- Usually 1 question every year, which is 4 marks.
- Energy levels and the spectral series are the regular ones.
- Hydrogen-like ions and the distance of closest approach fill the rest.
What the syllabus says
In the syllabus (Unit 18, Atoms and Nuclei): The alpha-particle scattering experiment, Rutherford’s model of the atom, the Bohr model, energy levels and the hydrogen spectrum.
Taken from the NTA syllabus for JEE Main 2027. See the full syllabus, unit by unit.
Formulas you must know by heart
| Bohr quantisation | mvr = nh/2π |
| Radius | rn = 0.53 n2/Z Å |
| Energy | En = −13.6 Z2/n2 eV |
| Speed | vn = 2.18 × 106 Z/n m/s |
| Energy relations | KE = −E, and U = 2E |
| Rydberg formula | 1/λ = RZ2(1/n12 − 1/n22) |
| Rydberg constant | R = 1.097 × 107 m−1 |
| Series | Lyman n1 = 1, Balmer n1 = 2, Paschen n1 = 3 |
| Number of spectral lines | n(n − 1)/2 |
| Distance of closest approach | r = 2kZe2/E, so r ∝ 1/E |
The two energy relations in the middle are worth holding on to. The kinetic energy is the total energy with the sign flipped, and the potential energy is twice the total energy. Any one of the three gives you the other two at once.
Ten questions. Give yourself ten minutes.
Write your answers down before you scroll. A question you looked up is a question you have not answered.
Q1. The energy of the n = 3 level of the hydrogen atom is
- (a) −13.6 eV
- (b) −3.4 eV
- (c) −1.51 eV
- (d) −0.85 eV
Q2. The first line of the Balmer series of hydrogen has a wavelength of about
- (a) 656 nm
- (b) 486 nm
- (c) 121 nm
- (d) 365 nm
Q3. A hydrogen atom in the n = 4 state returns to the ground state. The number of different spectral lines it can emit is
- (a) 3
- (b) 4
- (c) 6
- (d) 10
Q4. The ground state energy of a singly ionised helium atom is
- (a) −13.6 eV
- (b) −27.2 eV
- (c) −54.4 eV
- (d) −3.4 eV
Q5. The radius of the first orbit of a singly ionised helium atom is
- (a) 0.53 Å
- (b) 0.265 Å
- (c) 1.06 Å
- (d) 2.12 Å
Q6. In the Bohr model, the ratio of the kinetic energy of the electron to its total energy is
- (a) 1
- (b) −1
- (c) 2
- (d) −2
Q7. The potential energy U of the electron is related to its total energy E by
- (a) U = E
- (b) U = 2E
- (c) U = −2E
- (d) U = E/2
Q8. The distance of closest approach of an alpha particle to a nucleus varies with the kinetic energy E of the particle as
- (a) proportional to E
- (b) proportional to 1/E
- (c) proportional to E2
- (d) proportional to √E
Q9. The series limit of the Balmer series of hydrogen lies at a wavelength of about
- (a) 364.6 nm
- (b) 656 nm
- (c) 91.2 nm
- (d) 820 nm
Q10. The Bohr model is unable to explain
- (a) the hydrogen spectrum
- (b) the spectra of atoms having more than one electron
- (c) the Rydberg formula
- (d) the ionisation energy of hydrogen
Answer key, with a hint for each
| Q1 | (c) | E3 = −13.6/9. |
| Q2 | (a) | 1/λ = R(1/4 − 1/9) = 5R/36. This is the red H-alpha line. |
| Q3 | (c) | n(n − 1)/2 = 4 × 3/2. |
| Q4 | (c) | E ∝ Z2, so −13.6 × 4. |
| Q5 | (b) | r ∝ 1/Z, so 0.53/2. |
| Q6 | (b) | KE = −E, so the ratio is −1. |
| Q7 | (b) | U = 2E, and together with KE = −E it adds back to E as it must. |
| Q8 | (b) | All the kinetic energy turns into electrostatic potential energy, so a faster particle gets closer. |
| Q9 | (a) | The limit is the jump from infinity to n = 2, so 1/λ = R/4. |
| Q10 | (b) | It works beautifully for one electron and fails as soon as electrons start repelling each other. |
Now mark yourself honestly
JEE Main marks the way it marks. Use the same rule here:
- +4 for a right answer
- −1 for a wrong one
- 0 for a blank
So ten questions here are out of 40. In the real paper, 25 Physics questions are out of 100.
If you scored 32 or more, the basics of this chapter are secure. Move to harder questions, not more of these.
If you scored below 24, do not feel bad about it. You have just found out something useful before the exam did. Go back to the formula table above, learn it properly, and sit these ten again tomorrow.
And if you guessed a few and they landed, count those as wrong. A guess that works once will not work in January.
The full chapter, on a clock
Ten questions tell you a little. Twenty-five tell you the truth.
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