Question

a) A freshly prepared sample of a certain radioactive isotope has an activity of 4.70×10^8Bq. After 4.00hours, its activity is 1.90×10^8Bq (1 becquerel = 1 decay per second). Find the decay constant and half-life of the sample.

b) Most solar radiation has a wavelength of 1μm or less. What energy gap should the material in a solar cell have in order to absorb this radiation?

c) The refractive index of moist air in the front of an aircraft is 1.023. Of the LIDAR system detects a return pulse from air resistance (wind shear) after 20.0μs, how far away is the wind shear? Assume the correction for the air speed of the aircraft is negligible.

Answer 1

a)

$\frac{A}{A_0}=2^{-\frac{t}{T}},$

$T=tlog_2\frac{A_0}{A}=4log_2\frac{4.70\cdot10^8}{1.90\cdot10^8}=5.23~h.$

$\lambda=\frac{ln2}{T}=\frac{ln2}{5.23\cdot3600}=36,8\cdot 10^{-6} ~s^{-1}.$

b)

$E=\frac{hc}{\lambda}=\frac{6.63\cdot10^{-34}\cdot3\cdot10^8}{10^{-6}}=2\cdot10^{-19}~J.$

c)

$l=\frac cn\cdot\frac t2=\frac{2,998\cdot10^8}{1.023}\cdot\frac{20\cdot10^{-6}}{2}=2931~m.$