Dual Nature Of Radiation And Matter

The correct answer is option (C): electron
For a particle, de-Broglie wave length,

Kinetic energy,

Then,
so, Since an electron has the smallest mass, it also has the greatest de-Broglie wavelength.

Step 1: Understanding the Concept:
Planck's constant ( ) appears in the equation . We can determine its units by analyzing its dimensions.
Step 2: Detailed Explanation:
The unit of Planck's constant is Joule-second (J s).

• Angular Momentum ( ): . Units are , which is equivalent to .
• Moment of force (Torque): (or Joule).
• Power: (Watt).

According to Bohr's quantization rule, , which directly shows that and must have the same units.
Step 3: Final Answer:
The correct option is (c).

Step 1: Understanding the Concept:
A photon is a quantum of electromagnetic radiation. It carries momentum which is related to its wavelength .
Step 2: Detailed Explanation:
The momentum of a photon is given by . According to de Broglie's hypothesis, the wavelength of any particle (including a photon) is . Substituting into the de Broglie equation: $ \lambda' = \lambda$.

Step 1: Understanding the Concept:
The stopping potential (cut-off voltage) is the negative potential applied to the collector plate that just stops the fastest-moving photoelectrons.
Step 2: Detailed Explanation:
The maximum kinetic energy ( ) is equal to the work done by the stopping potential to stop the electron: $ V_0 = 1.5\text{ V} $
Step 3: Final Answer:
The kinetic energy is 1.5 eV.

Step 1: Understanding the Concept:
Einstein's photoelectric equation relates the energy of the incident photon to the work function and the maximum kinetic energy of the electron: .
Step 2: Detailed Explanation:
Since , we can rewrite the equation as: $ y = mx + c m = \frac{h}{e} h/e$.