0.5x = 0.0625
x log(0.5) = log(0.0625)
-0.30103 x = -1.20412
x = 1.20412 / 0.30103
x = 4
===========================
Check:
1/2 x 1/2 x 1/2 x 1/2 = 1/16 = 0.0625 yay!
Convert the percent to a decimal or fraction (0.125, or 1/8), and solve the equation:(1/2)^x = 1/8 (using "^" for power)
or:
0.5^x = 0.125
In this case, you can solve the problem by inspection (just try out different powers). In more difficult cases, where the solution ISN'T an integer, you can use logarithms (basically you divide the logarithm of 0.125 by the logarithm of 0.5).
3.125 percent of a sample is one 32nd of a sample. In the half-life scale it is the fifth half-life. (1/2, 1/4, 1/8, 1/16, 1/32, 1/64, 1/128, etc.)
four
the half-life
The half-life of a radioactive isotope is defined as the time taken for the isotope to decay to half of its initial mass. So to decay to 50 percent of its initial mass will take one half-life of the isotope. One half-life of the isotope is 10 hours so the time taken to decay is also 10 hours.
Their percent natural abundances are Ru-85 (72. 2 percent) and Ru-87 (27. 8 percent). Ru-85 and Ru-87 are the only naturally occurring isotopes of Rubidium out of its 35 known isotopes.
Natural uranium contains approx 0.7 percent U235, the rest U238. The 235 is the useful fissile isotope. Some reactors using graphite or heavy water can use natural uranium, but light water reactors need to have the U235 proportion increased to about 4 percent. this is called enrichment.
The idea is to convert the percent to a fraction (divide it by 100), and then solve the equation: (1/2)^x = (that fraction) (Note: Using "^" for "power".) In the general case, solving this equation requires logarithms. But in this specific case, you can just try out different whole numbers for "x". # 1/2 lives vs fraction 1 0.5 2 0.25 3 0.125 4 0.0625 5 0.03175 6 0.015875 The answer falls between 5 and 6 half lives, closer to 5.
That is done to calculate the weighted average.
Calculation of the atomic weight of an element having many isotopes:ia - atomic mass of the isotope a x percent concentration of the isotope in the elementib - atomic mass of the isotope b x percent concentration of the isotope in the elementic - atomic mass of the isotope c x percent concentration of the isotope in the element...........................................................................................................................iz - mass of the isotope z x percent concentration of the isotope in the elementMake the sum: I = ia + ib + ic + ..... izThe atomic weight of the element is: I/100 (the term weight is recommended by IUPAC in this case).
5%
19.9
248.90
Uranium 235 is 0.7 percent of natural uranium and is fissile
12.5% is remaining.
Carbohydrate analysis.
a sample is brought to the laboratory and the chemist determines the percentage of the daughter isotope is 87.5%. if the half-life of the isotope is 150 million years, how old is the sample?
profitability analysis
It will take between 450 and 525 years.
Take percent abundance times atomic mass for each isotope then add all up for average atomic mass.