The wavelength of an electron of kinetic energy 4.50×10⁻²⁹ J is _________ × 10⁻⁵ m. (Nearest integer)
Given : mass of electron is 9×10⁻³¹ kg, h =6.6×10⁻³⁴ J s

Solution

Chemistry ma’am · 4 steps

Turn kinetic energy into momentum with p = √2mK, then de Broglie gives the wavelength.

1. Momentum from energy. Kinetic energy is K = p²/2m, so p = √2mK. Put that into the de Broglie relation λ = h/p.

   λ = h/√2mK

2. Find the momentum. 2mK = 2 × 9 × 10⁻³¹ × 4.50 × 10⁻²⁹ = 81 × 10⁻⁶⁰. Its square root is p = 9 × 10⁻³⁰ kg m s⁻¹.
3. Divide. λ = (6.6 × 10⁻³⁴)/(9 × 10⁻³⁰) = 0.733 × 10⁻⁴ m = 7.33 × 10⁻⁵ m.
4. So. The wavelength is 7.33 × 10⁻⁵ m, which rounds to 7.

The common slip: 10. Dropping the 2 and using √mK gives λ ≈ 10.4 × 10⁻⁵ m, which rounds to 10, not 7.

The idea to keep. When the question gives kinetic energy instead of speed, use λ = h/√2mK directly. Write 2mK as a perfect square in powers of ten so the root comes out cleanly.

Answer from the NTA final answer key. Solution by PrepWiser.