A photon falls through a height of 1   km through the earth's gravitational field. To calculate the change in its frequency, take its mass to be h v / c 2 . The fractional change in frequency v is close to

Step-by-step solution

A photon of mass m and frequency v falls through a height H through the earth's gravitational field as shown in figure below. When the photon falls through the earth's gravitational field, then it is gains extra energy. Therefore, Final photon energy = Initial photon energy + Increase in energy ⇒ h v ' = h v + m g H = h v + h v c 2 . g H = h v 1 + g H c 2 So, f ' - f f = fractional change in frequency = g H c 2 = 10 × 1000 3 × 10 8 2 = 10 9 × 10 - 13 .