A photon of 640 nm is released from the surface of a neutron star of radius 10 km and a mass of 6 x 1030 kg. What will be the redshifted frequency detected far away from the neutron star due to its gravity?

A photon of 640 nm is released from the surface of a neutron star of radius 10 km and a mass of 6 x 1030 kg. What will be the redshifted frequency detected far away from the neutron star due to its gravity?

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Question

A photon of 640 nm is released from the surface of a neutron star of radius 10 km and a mass of 6 x
1030 kg. What will be the redshifted frequency detected far away from the neutron star due to its
gravity?

Expert Solution

Concept and Principle:

Gravitational redshift takes place when a photon leaves a gravitational well. As per general relativity due to space-time curvature, the frequency of the photon will reduce as it moves away from a gravitational source. This causes the gravitational redshift.

The gravitationally redshifted frequency is given by,

$\begin{array}{rcl} λ_{obs} & = & \frac{λ_{rest}}{\sqrt{1 - \frac{2 GM}{{rc}^{2}}}} \end{array}$

Here λ_restis the wavelength at the source, G is Newton’s gravitational constant, M is the mass of the object, r is the photon’s starting distance from M, and c is the speed of light.