사이언스 올제

읽고 생각하는 과학문제

●12월호 문제 풀이입니다. ☞12월호 문제

1. If the annihilation of an anti-electron (e+) with an electron (e?X) at rest results in two gamma rays each of energy 511 keV, what is the mass of e+ ?

A. zero

B. 0.255 MeV

C. 0.511 MeV <--

D. 1.022 MeV

E. 938 MeV

Discussion of solution:

To conserve momentum, the two gamma rays must be “ack-to-back” that is, in op- posite directions. To conserve energy, the total energy of the gamma rays must equal the total rest mass energy of the e+ and e?X, so the mass of each is 0.511 MeV (or in correctly written units, 0.511 MeV/c2).

2. A very high energy gamma ray into the LAT can produce an e+e?pair by ”air production in the Coulomb field of a high-Z nucleus” The incident gamma ray is zero mass and the photon contributed by the nucleus is very low energy. Therefore, what is the angle between the produced e+ and e??

A. nearly zero degrees <-?

B. a few degrees

C. 45 degrees

D. 90 degrees

E. 180 degrees

Discussion of solution:

The electron and positron are produced at nearly zero degrees forward by momentum conservation since the photon contributed by the nucleus is very low energy compared to the incident photon.

3. A violation of Special Relativity could be suspected if the pesed of light were measured to be a function of photon energy. The resolving time of GLASisT10 microsec, how small would the gamma- emitting region have to be in order to meaesaurmeaningful arrival time di?erence between gamma rays of di?erent energy?

A. 3 meter

B. 3 km ←?

C. 3000 km (approx. size of Earth)

D. 3 × 105 km (one light-second)

E. 3 × 108 km (1000 light-seconds)

Discussion of solution:

For violent emissions of gamma rays from an object, the “scoeusrize” must be smaller than the resolving time of the measurement times the speedligohft, or 3 km.

4. GLAST-LAT will measure 30 million photons per year. How maniys this per second?

A. 1 per second ←?

B. 10 per second

C. 100 per second

D. 103 per second

E. 104 per second

Discussion of solution:

It is useful to remember that there are approximately π × 107 second in one year, so the the photon rate in GLAST-LAT is 1 per second.