Derivation of gravitational redshift: Mass of a photon?

[SgrA*]

This is not exactly a homework question.

In a physics textbook, they derive an expression for gravitational redshift of a photon emitted by a star at a large distance from the source by taking photon as a mass traveling up, against a gravitational potential and hence expending its electromagnetic/quantum energy. The mass of the photon is taken to be:

$m = \frac{h\nu}{c^{2}}.$​

According to that equation, the mass of an X-ray photon of $10^{21} Hz$ would be about 8 times mass of an electron.

Is this treatment appropriate?

PS: I'm aware that the "accepted" derivation for gravitational redshift involves general relativity, but the expression derived in this text is a special case of that expression.

 

[mfb]

If you replace m by the energy E, you get a correct approach, so where is the point of using a relativistic mass...
Anyway, it gives correct results.

A photon with that frequency (I would call it gamma instead of X-ray, but that does not matter) has more energy than an electron at rest, indeed.