Chemistry · Structure Of Atom · NEET
m is the electron's mass, v is its speed, and r is the orbit radius. The product mvr is called angular momentum — it measures how much 'spinning motion' the electron has around the nucleus. Bohr said this value is not free to be anything. It must equal a whole number n times the fixed amount h/2π. So the electron can only sit in orbits where this rule is obeyed.
Bohr assumed it as a postulate — a starting rule he could not prove but that made the model work. Later, de Broglie explained it: the electron behaves like a wave, and only whole numbers of wavelengths fit around a circular orbit. That whole-number fitting is exactly what forces mvr to be a whole-number multiple of h/2π. For NEET, remember it as Bohr's postulate; de Broglie gives the deeper reason.
n is called the principal quantum number and it counts which orbit the electron is in (1st, 2nd, 3rd...). There is no orbit 'one and a half', so n can only be 1, 2, 3, 4 and so on. If you ever see n = 0 or a fraction in an option, it is wrong for a Bohr orbit.
Put n = 1 (the first orbit, closest to the nucleus). Then mvr = 1 × h/2π = h/2π. This is the lowest allowed value. The next orbit (n = 2) has 2 × h/2π, then 3 × h/2π, and so on. The values go up in equal steps of h/2π.
Planck's constant h has units of joule-second (J·s), which is the same as kg·m²/s. Angular momentum mvr also works out to kg·m²/s (mass × speed × radius). Because both sides of mvr = nh/2π have the same units and n is just a number, the equation is unit-consistent. This is a quick way to check a formula is not garbled.
Bohr had a few postulates. One says the electron moves in fixed circular orbits without losing energy (stationary states). Another says energy is emitted or absorbed only when the electron jumps between orbits. The quantisation rule mvr = nh/2π is the postulate that decides WHICH orbits are allowed. All three work together, but this one is the maths that picks the special orbits.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
No. Bohr's mvr = nh/2π uses n and is an older, simpler idea. The quantum-mechanical orbital angular momentum uses the azimuthal quantum number l and equals √(l(l+1))·h/2π. NEET tests both, so check which model the question is using — if it mentions 'Bohr orbit', use nh/2π.
No. mvr = nh/2π contains no Z. Only n matters. In contrast, the radius, velocity and energy of the orbit do depend on Z. This is a common trap point.
It is 2 × h/2π = h/π. Numerically, h/2π ≈ 1.05 × 10⁻³⁴ J·s, so for n = 2 it is about 2.1 × 10⁻³⁴ J·s.
Bohr assumed it as a postulate in 1913. de Broglie later (1924) gave the reason: the electron is a wave, and a whole number of wavelengths must fit around the orbit, which forces the nh/2π rule.
