Question

Radiometric dating is a technique used to find the age of materials on Earth, using the concept of radioactive decay (by measuring the relative abundance of the parent and daughter nuclei). One example of this is Uranium-Thorium dating, used for dating sediments, wherein Uranium-238 goes through a single alpha decay to give Thorium-234:
${}^{238}U{\to }^{234}Th+\alpha ,$
What will the Q-value of the process be?
Things you will need:

• A. 4.58 MeV
• B. 4.72 MeV
• C. 5.03 MeV
• D. 4.25 MeV

Answer 1

The correct option is D 4.25 MeV

The total rest masses of the products is $m{(}^{234}Th)+m{(}^{4}He)=234.04363u+4.00260u=238.04623u,$
Which is less than that of the parent nucleus, $m{(}^{234}U)=238.0508u.$
This loss in rest mass will result in a loss in corresponding energy, as given by 'the most famous equation' $E=m{c}^2,$ which is what we call the Q-Value!
Therefore, $Q-Value=\left[m{(}^{238}U\right)-\left\{m{(}^{234}Th\right)+m{(}^{4}He\left)\right\}]\times c^2$
$=[238.043553u-(234.04363u+4.00260u\left)\right]\times 931\frac{MeV}{u}$
$=\begin{array}{c}4.25MeV\end{array}$.