1. Write balanced equations for each of the following processes.
a. Chromium- 51, which targets the spleen and is used as a tracer in studies of red blood cells, decays by electron capture.
b. Iodine-131, used to treat hyperactive thyroid glands, decays by producing a beta particle.
2. In each of the following nuclear reactions, supply the missing particle?
a. ^60Co -> ^60Ni + ?
b. ^97Tc + ? -> ^97Mo
c. ^99Tc -> ^99Ru + ?
d. ^239Pu -> ^235U + ?
3. A chemist wishing to do an experiment requiring 47Ca (half life = 4.5 days) needs 5.0ìg of the
nuclide. What mass of 47Ca must be ordered if it takes 48 h for delivery from the supplier? Assume that the atomic mass of ^47Ca iis 47.0
4. What is the ratio of ^209Pb/^238U by mass in a rock that is 4.5x10^9 years old? (For 238 U, t1/2= 4.5x10^9 years)
Please help me.
1a. The decay of Chromium-51 by electron capture can be represented by the balanced equation:
^51Cr + e- -> ^51V
To balance the equation, we need to make sure that the number of protons and neutrons are equal on both sides.
1b. The decay of Iodine-131 by producing a beta particle can be represented by the balanced equation:
^131I -> ^131Xe + e-
To balance the equation, we need to make sure that the number of protons and neutrons are equal on both sides.
2a. In the reaction ^60Co -> ^60Ni + ?, we need to determine the missing particle. In this case, the missing particle is a gamma ray (γ). The balanced equation would be:
^60Co -> ^60Ni + γ
2b. In the reaction ^97Tc + ? -> ^97Mo, we need to determine the missing particle. In this case, the missing particle is an electron (e-). The balanced equation would be:
^97Tc + e- -> ^97Mo
2c. In the reaction ^99Tc -> ^99Ru + ?, we need to determine the missing particle. In this case, the missing particle is a gamma ray (γ). The balanced equation would be:
^99Tc -> ^99Ru + γ
2d. In the reaction ^239Pu -> ^235U + ?, we need to determine the missing particle. In this case, the missing particle is an alpha particle (α). The balanced equation would be:
^239Pu -> ^235U + α
3. To determine the mass of ^47Ca needed for the experiment, we can use the equation for radioactive decay:
N = N0 * (1/2)^(t/t1/2)
where N is the final amount of the nuclide, N0 is the initial amount of the nuclide, t is the time elapsed, and t1/2 is the half-life of the nuclide.
First, we need to determine the initial amount of ^47Ca (N0). We can use the equation:
N0 = (mass / atomic mass) * Avogadro's number
where mass is the desired mass of ^47Ca and atomic mass is the atomic mass of ^47Ca.
Then, we can substitute the values into the equation for N and solve for the final amount (N) when t = 48 hours.
Finally, we can rearrange the equation to solve for the mass:
mass = (N / Avogadro's number) * atomic mass
4. The ratio of ^209Pb/^238U by mass in a rock that is 4.5x10^9 years old can be determined based on the concept of radioactive decay and the half-lives of ^238U and ^209Pb.
Using the equation N = N0 * (1/2)^(t/t1/2), we can calculate the ratio of the number of atoms of ^209Pb to ^238U after 4.5x10^9 years.
Next, we can determine the masses of ^209Pb and ^238U by multiplying the respective number of atoms by their respective atomic masses.
Finally, we can calculate the ratio of the masses by dividing the mass of ^209Pb by the mass of ^238U.