Question

A sub-atomic particle of mass \( 10^{-30} \) kg is moving with a velocity of \( 2.21 \times 10^6 \) m/s. Under the matter wave consideration, the particle will behave closely like            (h = \( 6.63 \times 10^{-34} \) J.s)

• A. Infra-red radiation
• B. X-rays
• C. Gamma rays
• D. Visible radiation

Hint:

The de Broglie wavelength can be used to calculate the behavior of particles as waves. If the wavelength is on the order of \( 10^{-10} \) m, the particle behaves like X-rays.

Answer 1

The Correct Option is B

The de Broglie wavelength, \(\lambda\), describes the behavior of a sub-atomic particle as a matter wave. It is calculated using the formula: \(\lambda = \frac{h}{mv}\)

The variables are defined as:

• \(h = 6.63 \times 10^{-34}\) J·s (Planck's constant).
• \(m = 10^{-30}\) kg (particle mass).
• \(v = 2.21 \times 10^6\) m/s (particle velocity).

Substituting these values yields:

\(\lambda = \frac{6.63 \times 10^{-34}}{10^{-30} \times 2.21 \times 10^6}\)

The calculation results in:

\(\lambda = \frac{6.63 \times 10^{-34}}{2.21 \times 10^{-24}}\)

\(\lambda \approx 3.00 \times 10^{-10}\) meters, equivalent to 0.3 nanometers.

This calculated wavelength falls within the typical range of X-rays (0.01 to 10 nanometers). Therefore, when considered as a matter wave, the particle exhibits behavior similar to X-rays.

Conclusion: Under matter wave consideration, the particle's behavior is analogous to that of X-rays.