1. which of the following nuclear equations is correctly balanced? (choices attached) 2. the half-life of thorium-234 is 24 days. if you have a 42.0 g sample of thorium-24, how much will remain after 72 days? a. 42.0 g b. 21.0 g c. 10.5 g d. 5.25 g 3. it takes 5.2 min for a 4.0 g sample of francium-210 to decay until only 1.0 g is left. what is the half-life of francium-210? a. 1.3 min b. 2.6 min c. 5.2 min d. 7.8 min

1. Balancing nuclear equations

Explanation:

The main point to remember in balancing nuclear equations is that the sums of the superscripts (the mass numbers) and the subscripts (the nuclear charges) must balance.

Mass numbers: 37 + 0 = 37; balanced.

Charges: 18 + 1 = 17; balanced

B is wrong. Mass numbers not balanced. 6 +2(1) ≠ 4 + 3.

C is wrong. Mass numbers not balanced. 254 + 4 ≠ 258 + 2(1).

D is wrong. Mass numbers not balanced. 14 + 4 ≠ 17 + 2.

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2. Amount remaining

D. 5.25 g

Explanation:

The half-life of Th-234 (24 da) is the time it takes for half the Th to decay.  

After one half-life, half (50 %) of the original amount will remain.  

After a second half-life, half of that amount (25 %) will remain, and so on.

We can construct a table as follows:  

  No. of                  Fraction       Amount  

half-lives   t/(da)  remaining  remaining/g  

      1             24            ½                21.0  

      2            48            ¼                10.5  

      3             72           ⅛                 5.25  

      4             96          ¹/₁₆                 2.62  

We see that 72 da is three half-lives, and the amount of Th-234 remaining is 5.25 g.  

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3. Calculating the half-life

a. 2.6 min

Explanation:

The fraction of the original mass remaining is 1.0 g/4.0 g ≈ ¼.

We saw from the previous table that it takes two half-lives to decay to ¼ of the original amount.

2 half-lives = 5.2 min       Divide both sides by 2

  1 half-life = 5.2 min/2 = 2.6 min

the answer is 75.0%.