Question

Identify the correct statement/s from the following A. A group of waves need not have same velocity as the waves themselves.
B. Amplitude of de-Broglie wave of a particle reflects the probability that it will be found at a particular place at a particular time.
C. “If phase velocity varies with wavelength different individual waves proceed together” is called dispersion.
D. $V_{p}=\dfrac{\omega}{k}$ where \(V_p\) is phase velocity.
E. $V_{g}=\dfrac{\Delta k}{\Delta \omega}$ is group velocity. Choose the correct answer from the options given below:

• A. A, B, C only
• B. C, D, E only
• C. A, B, D only
• D. B, D, E only

Hint:

Group velocity is \(\dfrac{d\omega}{dk}\), not \(\dfrac{dk}{d\omega}\).

Answer 1

The Correct Option is C

Concept:
Wave mechanics explains phase velocity, group velocity and matter waves.
Step 1:
Group velocity and phase velocity are generally different. Thus A is correct.
Step 2:
Amplitude squared of de-Broglie wave gives probability density. Thus B is correct.
Step 3:
Dispersion occurs when phase velocity changes with wavelength. Thus C is correct. Phase velocity: \[ V_p=\frac{\omega}{k} \] Thus D is correct.
Step 4:
Correct relation is: \[ V_g=\frac{\Delta \omega}{\Delta k} \] Thus E is incorrect.
Step 5:
Correct statements are: \[ A,\quad B,\quad D \] \[ \boxed{\text{Correct Option = (3)}} \]