Physics 2007 JAMB Past Questions - Question 12: A photon of wavelenght 6.0 x 107m behaves like a particle of a certain mass. the value of that mass is

Correct Answer

C

Explanation

The behavior of a photon as a particle with mass can be described using the concept of relativistic mass. The energy (E) of a photon is given by the equation:

E = hf

Where:
E is the energy of the photon
h is Planck's constant (approximately 6.626 x 10^-34 J·s)
f is the frequency of the photon

The speed of light (c) is related to the wavelength (λ) and frequency (f) of a photon through the equation:

c = λf

Now, if you're given the wavelength (λ) of a photon, you can calculate the frequency (f) by rearranging the equation:

f = c / λ

Given that the wavelength (λ) is 6.0 x 10^7 meters, and the speed of light (c) is approximately 3.00 x 10^8 meters per second, you can calculate the frequency (f):

f = (3.00 x 10^8 m/s) / (6.0 x 10^7 m) = 5.0 Hz

Now, you can find the energy (E) of the photon using the equation E = hf:

E = (6.626 x 10^-34 J·s) * (5.0 Hz) = 3.313 x 10^-34 J

The energy of the photon is approximately 3.313 x 10^-34 joules. This energy can also be thought of as the rest energy of a particle with mass (m) using Einstein's mass-energy equivalence principle (E=mc^2), where c is the speed of light:

E = mc^2

3.313 x 10^-34 J = (m) * (3.00 x 10^8 m/s)^2

Now, solve for m (the mass of the particle):

m = (3.313 x 10^-34 J) / [(3.00 x 10^8 m/s)^2] = 3.682 x 10^-51 kg

So, the mass of the particle associated with a photon of wavelength 6.0 x 10^7 meters is approximately 3.682 x 10^-51 kilograms.