Question

3. Write the Expression for the momentum of a photon in in terms of wavelength .. How much is the rest mass of the photon Calculate the relativistic mass of a photon of wavelength5000A​

Answer 1

Explanation:

AS we  know,

p=λh=(5000×10−106.6×10−34=1.3×10−27kg−m/s

Strategy

Finding the photon momentum is a straightforward application of its definition: p=hλp=hλ. If we find the photon momentum is small, then we can assume that an electron with the same momentum will be nonrelativistic, making it easy to find its velocity and kinetic energy from the classical formulas.

Solution for Part 1

Photon momentum is given by the equation: p=hλp=hλ.

Entering the given photon wavelength yields

p=6.63×10−34 J ⋅ s500×10−9 m=1.33×10−27 kg⋅ m/sp=6.63×10−34 J ⋅ s500×10−9 m=1.33×10−27 kg⋅ m/s

Solution for Part 2

Since this momentum is indeed small, we will use the classical expression p = mv to find the velocity of an electron with this momentum. Solving for v and using the known value for the mass of an electron gives

v=pm=1.33×10−27 kg⋅ m/s9.11×10−31 kg=1460 m/s≈1460 m/sv=pm=1.33×10−27 kg⋅ m/s9.11×10−31 kg=1460 m/s≈1460 m/s

Solution for Part 3

The electron has kinetic energy, which is classically given by KEe=12mv2KEe=12mv2.

Thus, KEe=12(9.11×10−3 kg