A sub-atomic particle of mass 10⁻³⁰ kg is moving with a velocity 2.21 × 10⁶ m / s. Under the matter wave consideration, the particle will behave closely like (h=6.63 × 10⁻³⁴ J . s)

Solution

Physics sir · 3 steps

Find the particle's de Broglie wavelength, then see which part of the EM spectrum has that wavelength.

1. Matter wave. A moving particle has a de Broglie wavelength set by its momentum p = mv.

   λ = h/mv = (6.63 × 10⁻³⁴)/(10⁻³⁰ × 2.21 × 10⁶) = (6.63 × 10⁻³⁴)/(2.21 × 10⁻²⁴) = 3 × 10⁻¹⁰ m

2. Read the value. λ = 3 × 10⁻¹⁰ m = 0.3 nm = 3 Å. This is about the size of an atom.

   Radiation	Typical wavelength range	Contains 0.3 nm?
   Gamma rays	below about 0.01 nm	no, too short
   X-rays	about 0.01 nm to 10 nm	yes
   Visible	400 nm to 700 nm	no, far too long
   Infra-red	700 nm to 1 mm	no, far too long

3. So. A wavelength of 3 × 10⁻¹⁰ m lies in the X-ray region, so the particle behaves like X-rays, option (a).

The idea to keep. For matter waves, compute λ = h/mv first, then compare it with the EM spectrum. Angstrom-scale wavelengths mean X-rays, and that is why electron beams can do diffraction like X-rays do.

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