Question

If \( \lambda \) and \( K \) are de Broglie wavelength and kinetic energy, respectively, of a particle with constant mass. The correct graphical representation for the particle will be:

• A.
• B.
• C.
• D.

Hint:

The de Broglie wavelength of a particle is inversely proportional to the square root of its kinetic energy. This leads to a curve where \( 1/K \) is plotted against \( \lambda \).

Answer 1

The Correct Option is A

For a particle with constant mass, the de Broglie wavelength \( \lambda \) and kinetic energy \( K \) are related by the equation: \[ \lambda = \frac{h}{\sqrt{2mK}}, \] where \( h \) is Planck's constant, \( m \) is the mass of the particle, and \( K \) is the kinetic energy. Since \( K \) is proportional to the inverse of \( \lambda^2 \), the relationship between \( \lambda \) and \( K \) will be a curve where \( \frac{1}{K} \) is plotted against \( \lambda \). This results in a curve that decreases as \( \lambda \) increases, which matches option (1). Thus, the correct graphical representation is option (1).