Light from a massive star suffers ' gravitational red- shift 'i.e It'swavelength changes towards the red endto the gravitational attractionof the star. Obtain the formula for this gravitational red - shift using the simple consideration that a photon of frequency 'v' has energy 'hv'and mass (hv)/(c^(2)) . Estimate magnitude of the red - shift for light of wavelength 5000Åfrom a star of mass 10^(32) kg and radius 10^(6) km. (G = 6.67xx10^(-11)Nm^(2)kg^(-2),c=3.00xx10^(8)ms^(-1))

Light from a massive star suffers ' gravitational red- shift 'i.e It's

1.	Light from a massive star suffers ' gravitational red- shift 'i.e It'swavelength changes towards the red endto the gravitational attractionof the star. Obtain the formula for this gravitational red - shift using the simple consideration that a photon of frequency 'v' has energy 'hv'and mass (hv)/(c^(2)) . Estimate magnitude of the red - shift for light of wavelength 5000Åfrom a star of mass 10^(32) kg and radius 10^(6) km. (G = 6.67xx10^(-11)Nm^(2)kg^(-2),c=3.00xx10^(8)ms^(-1))
Answer» Solution :Given, `R=10^(6)km=10^(9)m` `lamda=5XX10^(-7)m` `M=10^(32)KG` `lamda^(-1)=(c+V)/(c) lamda` `Deltalamda=lamda^(1)-lamda=(c+v)/(c)lamda-lamda=(lamda/(c))v` but `1//2 mv^(2)=(GMm)/(r) "(m-mass of photon)"` `:. v = sqrt((2GM)/(r))` i.e., red shift `Deltalamda=(lamda/c)(sqrt((2GM)/r))=((5xx10^(-7))/(3xx10^(8)))sqrt((2xx6.67xx10^(-11)xx10^(32))/(10^(9)))` `=60.87xx10^(-10)m` `Deltax=60.87Å`