Light from a massive star suffers 'gravitational red shift' i.e.,… - Vidyadip

Question

Light from a massive star suffers 'gravitational red shift' i.e., its wavelength changes towards the red end due to the gravitational attraction of the star. Obtain the formula for this gravitational red shift using the simple consideration that a photon of frequency v has energy $\text{h}\nu$ (h=planck's constant) and mass $\frac{\text{h}\nu}{\text{c}^2}.$ Estimate the magnitude of the red-shift for light of wavelength $5000\mathring{\text{A}}$ from a star of mass $10^{32}kg$ and radius $10^6km. G = 6.67 \times 10^{-11}Nm^2 kg^{-2}$ and $C = 3 \times 108m s^{-1}$.

✓

Answer

$\text{h}\nu^{'}=\text{h}\nu-\frac{\text{GMh}\nu}{\text{Rc}^2}$i.e., $\nu'=\nu\Big(1-\frac{\text{GM}}{\text{c}^2\text{R}}\Big)$
where $\nu'$ is the shifted frequency.
Now, $\lambda'=\lambda\Big(1+\frac{\text{GM}}{\text{c}^2\text{R}}\Big)$ if $\frac{\text{GM}}{\text{Rc}^2}<1$
i.e., $\lambda'-\lambda=\frac{\lambda\text{GM}}{\text{c}^2\text{R}}=0.371\mathring{\text{A}}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from Gravitation→Gravitation — all question types→Physics STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

It is known that the period T of a magnet of magnetic moment M vibrating in a uniform magnetic field of intensity B depends upon M, B and I where I is the moment of inertia of the magnet about its axis of oscillations. Show that: $\text{T}=2\pi\sqrt{\frac{\text{I}}{\text{MB}}}$

Derive a relation for the time taken by a projectile to reach the highest point and the maximum height attained?

A particle starts from the origin, goes along the $X-$axis to the point $(20m, 0)$ and then returns along the same line to the point $(-20m, 0)$. Find the distance and displacement of the particle during the trip.

A stone tied to the end of a string 80cm long is whirled in a horizontal circle with a constant speed. If the stone makes 14 revolutions in 25s, what is the magnitude and direction of acceleration of the stone?

A uniform rod of length l is suspended by an end and is made to undergo small oscillations. Find the length of the simple pendulum having the time period equal to that of the rod.

Explain clearly, with examples, the distinction between: Magnitude of average velocity over an interval of time, and the average speed over the same interval. [Average speed of a particle over an interval of time is defined as the total path length divided by the time interval]. Show in both (a) and (b) that the second quantity is either greater than or equal to the first. When is the equality sign true? [For simplicity, consider one-dimensional motion only]

An aeroplane is flying in a horizontal direction with a velocity of 600km/ hr and at a height of 1960m. When it is vertically above the point A on the ground, a body is dropped from it. The body strikes the ground at point B. Calculate the distance AB.

On complete combustion a litre of petrol gives off heat equivalent to $3 \times 107J$. In a test drive a car weighing $1200kg$. including the mass of driver, runs $15km$ per litre while moving with a uniform speed on a straight track. Assuming that friction offered by the road surface and air to be uniform, calculate the force of friction acting on the car during the test drive, if the efficiency of the car engine were $0.5$

Two rods of the same area of cross-section, but of lengths $l_1$ and $l_2$ and conductivities $K_1$ and $K_2$ are joined in series. Show that the combination is equivalent of a material of conductivity, $\text{K}=\frac{\text{l}_1+\text{l}_2}{\Big(\frac{\text{l}_1}{\text{K}_1}\Big)\Big(\frac{\text{l}_2}{\text{K}_2}\Big)}$

When a system is taken through the process abc shown in figure. 80J of heat is absorbed by the system and 30J of work is done by it. If the system does 10J of work during the process adc, how much heat flows into it during the process?