The half-life for the α decay of uranium is 4.47 × 109 yr. determine the age (in years) of a rock specimen that contains 55.5% of its original number of atoms.

Explanation:

Half-life of uranium = years

First we have to calculate the rate constant, we use the formula :

Now we have to calculate the age of the sample:

Expression for rate law for first order kinetics is given by:

where,

k = rate constant  =

t = age of sample  = ?

a = let initial amount of the reactant  = 100

a - x = amount left after decay process  =

Now put all the given values in above equation, we get

Thus the age of a rock specimen that contains 55.5% of its original number of atoms is

the answer is definitely c.

scattering of light by tiny particles in air to produce the colors we see on sky, is dependent on the following factors:

(i) wavelength of light

(ii) size of the scattering particle  

(iii) distance traveled by light through the atmosphere.

according to rayleigh's law of scattering, the amount of scattering is inversely proportional to the fourth power of its wavelength. shorter the wavelength, greater is its scattering. hence violet/blue light is scattered more than red.

sun's light is a composite light ( visible light) with wavelengths in the range 400 nm (violet) to 700 nm (red). as sunlight passes through our atmosphere, the molecules of air scatter light according to their wavelengths. during sunrise and sunset, the sun's position is below the horizon. hence light from the sun travels a greater distance in the atmosphere when compared to its position a noon.

as sunlight enters the earth's atmosphere, blue light is scattered away and at the end of its journey in the sky, only red and orange wavelengths remain in the beam.

hence at sunrise and sunset, the sky appears reddish orange.