JEE Advanced 2026 · Paper 1

Consider a hydrogen atom with vₖ, rₖ, and Kₖ denoting the velocity, orbital radius and kinetic energy of the electron in the kᵗʰ orbit, respectively. The electron undergoes a transition from the nᵗʰ orbit, emitting radiation corresponding to the Lyman series. Considering h to be the Planck’s constant and ε₀ the permittivity of the free space, the correct statement(s) is/are:

1. AMagnitude of change in kinetic energy of electron can be expressed as h/(4π) |nvₙ/rₙ − v₁/r₁|.
2. BMagnitude of change in de Broglie wavelength of the electron can be expressed as e²/(4ε₀) |1/Kₙ − 1/K₁|.
3. CFrequency of the radiation emitted can be expressed as e²/(8πε₀h)(1/r₁ − 1/rₙ).
4. DMagnitude of change in total energy of the electron can be expressed as h/(2π) |v₁/r₁ − nvₙ/rₙ|.

The electric field associated with an electromagnetic wave travelling in vacuum is given by E₀ sin(3y + 4z + ωt) î, where ω is the angular frequency. All quantities are in SI units. The correct statement(s) about this wave is/are: [Given: speed of light in vacuum c = 3 × 10⁸ ms⁻¹.]

1. AThe wave is travelling in −1/5 (3ĵ + 4k̂) direction.
2. BThe magnitude of the wave vector is 0.5 m⁻¹.
3. CThe value of ω is 1.5 × 10⁹ rad s⁻¹.
4. DThe magnetic field associated with this wave is given by (E₀/c) sin(3y + 4z + ωt)(4ĵ − 3k̂).