Atomic Physics · Hydrogen Lyman Transition

Follow the electron inward and verify the true statements

In a Lyman-series emission, the hydrogen electron drops from the nth orbit to the first orbit. The Bohr relations connect orbit radius, speed, kinetic energy and emitted frequency, letting us test each proposed statement.

2026 Paper 1 Q5 · hydrogen transition to n = 1
Statement check
Initial orbit n 4
Bohr orbit structure
For hydrogen, rₖ scales as k², vₖ scales as 1/k, and Kₖ scales as 1/k².
Relationm vₖ rₖ = kh/(2π)
VerdictLyman: n → 1
Initial orbitelectron begins at n
Photon emittedenergy difference leaves as radiation
Final orbitLyman series ends at k = 1

Derivation path

01 / BOHR QUANTIZATION

Relate speed, radius and orbit number

The angular momentum condition gives m vk rk = kh/(2π). This is the key to statement A.

K = ½mv² = hkv/(4πr)
02 / KINETIC ENERGY

Change in kinetic energy matches statement A

Using Kk = hkvk/(4πrk), the magnitude of the change from n to 1 is exactly the expression in A.

|ΔK| = h/(4π)|nvn/rn − v1/r1|
03 / PHOTON FREQUENCY

Energy gap gives statement C

For a Bohr orbit, total energy E = −e²/(8πε₀r). The emitted photon frequency is |ΔE|/h.

ν = e²/(8πε₀h)(1/r₁ − 1/rₙ)
Correct statements
Statement A is true from Kk = hkvk/(4πrk).
Statement C is true from hν = En − E1.
Correct answer: A and C