Question

How can I calculate the wavelength of photon?

Answer 1

Hint: In this question, we will directly use the basic relation between speed, frequency and the wavelength of a given wave or radiation. Further, we will study the basic difference between speed and velocity. We will also study the basic definition of frequency, for our better understanding.

Formula used:
$f = \dfrac{c}{\lambda }$

Complete solution:
As we know, a photon can be defined as a type of elementary particle. Also, a photon is the quantum of the electromagnetic field; a photon includes electromagnetic radiation like light and radio waves, and is the force carrier for the electromagnetic force.

Now we know, there is a relation between the wavelength, speed of light c and frequency f. this relation is given by:
$f = \dfrac{c}{\lambda }$
We know the speed of light c is equal to$3 \times {10^8}m/s$.

Now, the above equation of frequency can also be written as:
$f = \dfrac{v}{\lambda }$
$\therefore \lambda = \dfrac{v}{f}$

Therefore, we get the required expression to calculate the wavelength of a photon.

Additional information:
We already know the basic difference between the terms speed and velocity i.e., speed is the measure of how fast an object can travel, whereas velocity tells us the direction of this speed. Here, speed is a scalar quantity that means that speed has only magnitude, whereas velocity is a vector quantity that means velocity has both magnitude as well as direction.

Now, the S.I unit of velocity is meter per second which is represented by m/sec.

Also, we know that the speed of sound is different in different mediums. Further, we know that the speed is more than the speed of sound is termed differently like- supersonic, hypersonic etc

Further, we know that the frequency is mostly defined as the number of waves that pass through a fixed point in a unit time. Also, the S.I unit of frequency is Hertz or it is represented by Hz and the unit of wavelength is meter or it is represented by m.

Note:
This question can be directly answered by knowing the basic relation between speed and wavelength. Also, we know speed does not have any direction unlike velocity therefore, we can say that speed cannot be negative. We must remember that the unit of speed and velocity is the same i.e., meter per sec or m/s.