328 6 Special Theory of Relativity
are the sole products of disintegration of a heavier object, what was the rest
mass, velocity and direction of motion?
[University of Bristol 1965]6.87 A V-type of event is observed in a bubble chamber. The curvature measure-
ments on the two tracks show that their momenta arep+= 1 .670 GeV/c and
p−= 0 .408 GeV/c. The angle contained between the two tracks isθ= 15 ◦.It
is obviously due to the decay of a neutral unstable particle. It is suspected that
it is due to the decay(a)K^0 →π++π−or(b)Λ→p+π−. Identify the
neutral particle.
6.88 Derive the formula in Problem 6.103 using the invariance of (ΣE)^2 −|Σp|^2
6.89 Calculate the maximum four momentum transfer to proton in the decay of
neutron at rest.
6.2.5 Transformation of Angles and Doppler Effect .......
6.90 Find the Doppler shift in wavelength ofHline at 6,563A emitted by a star ̊
receding with a relative velocity of 3× 106 ms−^1.
6.91 Certain radiation of a distant nebula appears to have a wavelength 656 nm
instead of 434 nm as observed in the laboratory. (a) if the nebula is mov-
ing in the line of sight of the observer, what is its speed? (b) Is the nebula
approaching or receding?
6.92 Show that for slow speeds, the Doppler shift can be approximated as
Δλ/λ=v/c
whereΔλis the change in wavelength.
6.93 A physicist was arrested for going over the railway level crossing on a motor-
cycle when the lights were red. When he was produced before the magistrate
the physicist declared that he was not guilty as red lights (λ=670 nm)
appeared green (λ=525 nm) due to Doppler Effect. At what speed he was
travelling for the explanation to be valid? Do you think such a speed is
feasible?
6.94 A spaceship is receding from earth at a speed of 0.21c. A light from the
spaceship appears as yellow (λ= 589 .3 nm) to an observer on earth. What
would be its color as seen by the passenger of the spaceship?
6.95 Find the wavelength shift in the Doppler effect for the sodium line 589 nm
emitted by a source moving in a circle with a constant speed 0.05cobserved
by a person fixed at the center of the circle.
6.96 A neutrino of energyE 0 and negligible mass collides with a stationary elec-
tron. Find an expression for the laboratory angle of emission of the electron
in terms of its recoil energyEand calculate its value whenE 0 =2 GeV and
E= 0 .5GeV