Special Theory of Relativity
29
11. A proton gains an energy of 1 electron volt (eV) or 1.6 × 10
–19
J when it
traverses a potential difference of 1 V. If the proton has a mass of
1.67 × 10
–27
k.g., what is the velocity of the proton which starts from rest
and traverses a potential difference of 10
9
V? What is the velocity of a
proton which comes out of the CERN super proton synchrotron with an
energy of 270 GeV (1 GeV is equal to 10
9
eV)?
12. A star is observed at the zenith taken to be the z-direction. If the star is
moving in the x-direction, and its radiation shows a redshift of 0.003 Å for
the H α Balmer line (λ = 6563Å), what is its velocity with respect to us?
If the star were moving towards us with the same speed, what would be
the observed wavelength for the H α line?
13. A charged particle can move in a material medium with a velocity greater
than the velocity of light in that medium. It polarizes the nearby atoms
which then emit radiation known as Cerenkov radiation. The envelope of
the spherical waves is a cone with the vertex at the charged particle and
whose surface makes an angle θ with the direction of motion of the particle.
Show that sin θ = c/nv, where v is the speed of the particle and n is the
refractive index of the medium (v ≥ c/n).
29
11. A proton gains an energy of 1 electron volt (eV) or 1.6 × 10
–19
J when it
traverses a potential difference of 1 V. If the proton has a mass of
1.67 × 10
–27
k.g., what is the velocity of the proton which starts from rest
and traverses a potential difference of 10
9
V? What is the velocity of a
proton which comes out of the CERN super proton synchrotron with an
energy of 270 GeV (1 GeV is equal to 10
9
eV)?
12. A star is observed at the zenith taken to be the z-direction. If the star is
moving in the x-direction, and its radiation shows a redshift of 0.003 Å for
the H α Balmer line (λ = 6563Å), what is its velocity with respect to us?
If the star were moving towards us with the same speed, what would be
the observed wavelength for the H α line?
13. A charged particle can move in a material medium with a velocity greater
than the velocity of light in that medium. It polarizes the nearby atoms
which then emit radiation known as Cerenkov radiation. The envelope of
the spherical waves is a cone with the vertex at the charged particle and
whose surface makes an angle θ with the direction of motion of the particle.
Show that sin θ = c/nv, where v is the speed of the particle and n is the
refractive index of the medium (v ≥ c/n).