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 measurements on the two tracks show that their momenta are p + = 1.670 GeV/c and
p − = 0.408 GeV/c. The angle contained between the two tracks is θ = 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 of H line at 6,563 ˚
A emitted by a star
receding with a relative velocity of 3 × 10
6 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 moving 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
where Δλ is the change in wavelength.
6.93 A physicist was arrested for going over the railway level crossing on a motorcycle 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 0.21 c. 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 0.05 c observed
by a person fixed at the center of the circle.
6.96 A neutrino of energy E 0 and negligible mass collides with a stationary electron. Find an expression for the laboratory angle of emission of the electron
in terms of its recoil energy E and calculate its value when E 0 = 2 GeV and
E = 0.5 GeV
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 measurements on the two tracks show that their momenta are p + = 1.670 GeV/c and
p − = 0.408 GeV/c. The angle contained between the two tracks is θ = 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 of H line at 6,563 ˚
A emitted by a star
receding with a relative velocity of 3 × 10
6 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 moving 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
where Δλ is the change in wavelength.
6.93 A physicist was arrested for going over the railway level crossing on a motorcycle 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 0.21 c. 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 0.05 c observed
by a person fixed at the center of the circle.
6.96 A neutrino of energy E 0 and negligible mass collides with a stationary electron. Find an expression for the laboratory angle of emission of the electron
in terms of its recoil energy E and calculate its value when E 0 = 2 GeV and
E = 0.5 GeV