35. Special Relativity

An astronaut travels to a star system 4.5 ly away at a speed of 0.90c. Assume that the time needed to accelerate and decelerate is negligible. How long does the journey take according to Mission Control on earth?

A cosmic ray travels 60 km through the earth's atmosphere in 400 μs, as measured by experimenters on the ground. How long does the journey take according to the cosmic ray?

You fly 5000 km across the United States on an airliner at 250 m/s. You return two days later at the same speed. Have you aged more or less than your friends at home?

Two events in reference frame S occur 10 μs apart at the same point in space. The distance between the two events is 2400 m in reference frame S'. What is the velocity of S' relative to S?

In an attempt to reduce the extraordinarily long travel times for voyaging to distant stars, some people have suggested traveling at close to the speed of light. Suppose you wish to visit the red giant star Betelgeuse, which is 430 ly away, and that you want your 20,000 kg rocket to move so fast that you age only 20 years during the round trip. How fast, as a fraction of c, must the rocket travel relative to earth?

A rocket is fired from the earth to the moon at a speed of 0.990c. Let two events be 'rocket leaves earth' and 'rocket hits moon.' In the earth's reference frame, calculate ∆x, ∆t, and the spacetime interval s for these events.

A rocket is fired from the earth to the moon at a speed of 0.990c. Let two events be 'rocket leaves earth' and 'rocket hits moon.' Repeat your calculations of part a if the rocket is replaced with a laser beam.

A hydrogen atom has orbital angular momentum 3.65 × 10⁻³⁴ J s. What is the atom's minimum possible energy? Explain.

How many lines of atoms would you expect to see on the collector plate of a Stern-Gerlach apparatus if the experiment is done with (a) lithium and (b) beryllium? Explain.

Identify the element for each of these electron configurations. Then determine whether this configuration is the ground state or an excited state. 1s² 2s² 2p⁵

Identify the element for each of these electron configurations. Then determine whether this configuration is the ground state or an excited state. 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d²

Draw a series of pictures, similar to Figure 41.21, for the ground states of Ca, Ni, As, and Kr.

An excited state of an atom has a 25 ns lifetime. What is the probability that an excited atom will emit a photon during a 0.50 ns interval?

1.0×10⁶ atoms are excited to an upper energy level at t = 0 s. At the end of 20 ns, 90% of these atoms have undergone a quantum jump to the ground state. What is the lifetime of the excited state?

A laser emits 1.0 × 10¹⁹ photons per second from an excited state with energy E₂ = 1.17 eV. The lower energy level is E₁ = 0 eV. What is the wavelength of this laser?