Question

The mass of a particle is 16 times heavier than another particle and they have the same kinetic energy. The de-Broglie wavelength of the lighter particle is:

• A. Same as the heavier particle’s wavelength
• B. 2 times the heavier particle’s wavelength
• C. 4 times the heavier particle’s wavelength
• D. \( \frac{1}{4} \) times the heavier particle’s wavelength

Hint:

For same kinetic energy, de-Broglie wavelength varies inversely as square root of mass.

Answer 1

The Correct Option is C

Step 1: De Broglie relation.
λ = h/√(2mK); at equal kinetic energy K, λ ∝ 1/√m.

Step 2: Mass relationship.
Heavier particle: m_H = 16 m_L.

Step 3: Wavelength ratio.
λ_L/λ_H = √(m_H/m_L) = √16 = 4.

Step 4: Interpretation.
The lighter particle has the longer wavelength.

Step 5: Conclusion.
λ_L = 4 λ_H.