Q. A photon traveling in the positive x-direction collides with a stationary free electron. The incident photon has a wavelength of 0.0310 nm. Post-collision, the electron moves at an angle 𝛼 below the positive x-axis, and the photon deflects at an angle 𝜃 = 66.3° above the positive x-axis. A) Calculate the angle 𝛼 (in degrees). B) Compute the velocity of the electron (in m/s). Solution:
What is a Periodic Function?
If the function 𝑓(𝑥) repeats it’s value after equal interval of x, then 𝑓(𝑥) is said to be a periodic function of x and the equal interval of x, is known as time period of the function 𝑓(𝑥).
𝑓(𝑥) = 𝑓(𝑥 + 𝑇) = 𝑓(𝑥 + 2𝑇 )=. . . . . . . . . . = 𝑓(𝑥 + 𝑛𝑇) =. . . . .
Here T is known as the time period of the function.
Types of Periodic Function :
Sinusoidal Periodic Function:
A sinusoidal function is a function that is like a sine or cosine functions. Sinusoidal functions are a specific type of periodic function. Period of Sine and Cosine is 2π.
If the function 𝑓(𝑥) repeats it’s value after equal interval of x, then 𝑓(𝑥) is said to be a periodic function of x and the equal interval of x, is known as time period of the function 𝑓(𝑥).
𝑓(𝑥) = 𝑓(𝑥 + 𝑇) = 𝑓(𝑥 + 2𝑇 )=. . . . . . . . . . = 𝑓(𝑥 + 𝑛𝑇) =. . . . .
Here T is known as the time period of the function.
Types of Periodic Function :
Sinusoidal Periodic Function:
A sinusoidal function is a function that is like a sine or cosine functions. Sinusoidal functions are a specific type of periodic function. Period of Sine and Cosine is 2π.
- Time Period of Sin (t) and cos (t) is T = 2𝜋
- Time Period of Sin (mt) and cos (mt) is T = 2𝜋/𝑚
Non- Sinusoidal Periodic Function:
A non-sinusoidal waveform is typically a periodic oscillation. Some examples are square waves, rectangle waves, triangular waves, saw tooth waves and trapezoid waves .
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