Astronomy 2 Questions

Q1. If the average household uses 1400 kW-hr per month, how long would the conversion of 1 kg of hydrogen to helium power an average household?

Q2. b. If you are cruising down the road at 50 mph and a policeman with a radar gun (wavelength 1 cm) reflects radar light off your bumper, what wavelength of radar light does he get back? Assume the policeman is stationary, and you are moving towards him. Light that gets reflected has twice as much shift as light that is just emitted, so use the formula for the shift of emitted light but multiply by two.

the fusion reaction of hydrogen into Helium is

$(^2_1) H +(^3_1) H = (^4_2) He + 17.59 MeV$

so for 2 atoms of H we have $17.59 MeV$

in 1 kg of Hydrogen (approx. 1 kmole) there are $Na (Avogadro number) = 6.023*10^{26}$ atoms

The energy released is

$E = Na/2* 17.59 MeV =6.023*10^{26}*17.59*10^6*1.6*10^{-19}/2 =8.47*10^{14}$ Joule

The energy for one house for one month

$E1 = 1400*10^3*3600 =5.04*10^9$

Total time is

$t = E/E1 =8.47*10^14/5.04*10^9 =1.68*10^5 months =168000 months = 14004 years$