Fermium-253 is a radioactive isotope of fermium that has a half-life of 3.0 days. A scientist obtained a sample that contained 2

Problem 2

You begin with 216 micrograms of Fermium - 253. After three days, the quantity halves, resulting in 108 micrograms left.

Another three days pass. Beginning with 108 micrograms, this amount gets halved again, leaving 54 micrograms.

Finally, after another three-day span, starting from 54 micrograms, you again halve this amount to reach 27 micrograms.

#days              Amount in micrograms

0                              216

3                               108

6                                54

9                                27

Problem One

Your example is Nitrogen. Begin by completing the table, then formulate some rules to help prepare for possible alternate elements in the test. This approach is quite useful.

Table

Bond               Energy Kj/Mol               Bond Length pico meters

N - N                 167                                                145

N=N                  418                                                125

N≡N                  942                                               110

Rules

As the number of bonds INCREASES, the energy within the bond also INCREASES

As the number of bonds INCREASES, the distance of the bond DECREASES.

1. Radioactive decay

The half-life of Fm-198 (3.0 days) represents the duration required for half of the Fm to decay.

After the first half-life, 50% of the initial amount remains.

Following a second half-life, only 25% of that initial mass stays, and this pattern continues.

The table can be outlined as follows:

 No. of                   Fraction         Amount

half-lives  t/days  remaining   remaining/µg

       2         6.0             ¼                  108

       3         9.0             ⅛                    54

2. Bond length and bond energy

The bond order indicates the number of electrons engaged in bonding between the two atomic nuclei.

As the number of bonding electrons rises, the nuclei experience a stronger pull toward each other (resulting in increased bond energy) and the bond length shortens.

A table can be devised as follows:

Bond  Bond energy/kJ·mol⁻¹  Bond length/pm

N-N                 167                                 145

N=N                 418                                 125

N≡N                 942                                 110