Question 30

A common example of alpha decay is $$^{238}_{92}$$U $$\to ^{234}_{90}$$Th $$+ _2$$He$$^4 + Q$$
Given:
$$^{238}_{92}$$U $$= 238.05060$$ u
$$^{234}_{90}$$Th $$= 234.04360$$ u
$$^4_2$$He $$= 4.00260$$ u and $$1$$u $$= 931.5$$ $$\frac{\text{MeV}}{c^2}$$
The energy released $$(Q)$$ during the alpha decay of $$^{238}_{92}$$U is _____ MeV.

Correct Answer: 4

$$\Delta m = m\left(^{238}_{92}\text{U}\right) - \left[m\left(^{234}_{90}\text{Th}\right) + m\left(^{4}_{2}\text{He}\right)\right]$$

$$\Delta m = 238.05060 - (234.04360 + 4.00260) = 238.05060 - 238.04620 = 0.00440\text{ u}$$

$$Q = \Delta m \times 931.5\text{ MeV} = 0.00440 \times 931.5 = 4.0986\text{ MeV}$$

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