Chapter 24: 24.143 CP (page 1108)

Plutonium-242decays to uranium-238by emission of an $α$ -particle with an energy of 4.853MeV. The ²³⁸U that forms unstable and emits a $γ$ -ray ( $λ = 0.02757 n m$ ).
(a) Write balanced equations for these reactions.
(b) What would be the energy of the-particle if ²⁴²P decayed directly to the more stable ²³⁸U?

Short Answer

Expert verified

(a) $_{94}^{249} P u \to_{92}^{238} U +_{2}^{4} α 238_{92} U \to 238_{92} U + γ$

(b) 4.989 MeV.

Step by step solution

Definition of Half-life

The time it takes for a given reactant's concentration to reach 50%its initial concentration is known as the half-life of a chemical reaction (i.e., the time taken for the reactant concentration to reach half of its initial value).

It's commonly represented in seconds and is denoted by the sign 't_1/2'.

Subpart (a)

Balanced equation

$_{94}^{249} P u \to_{92}^{238} U +_{2}^{4} α 238_{92} U \to 238_{92} U + γ$

Subpart (b)

To determine the energy in MeV we need to use the formula of $γ$ ray.

$E = \frac{h c}{λ}$

$E = \frac{h c}{λ} = \frac{(6.626 x 10^{- 34} J . s \times 2.99792 x 10^{8} m / s)}{(0.02747 \times 10^{- 9} m)} = 723.1 J = 0.0450 M e V (∵ 1 M e V = 1.60 \times 10^{- 13} J)$

Total Energy:

$E_{T} = 4.853 M e V + 0.0450 M e V \ hfill E_{T} = 4.989 M e V$

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Plutonium-242decays to uranium-238by emission of an α-particle with an energy of 4.853MeV. The 238U that forms unstable and emits a γ-ray (λ=0.02757nm).(a) Write balanced equations for these reactions.(b) What would be the energy of the-particle if 242P decayed directly to the more stable 238U?

Short Answer

Step by step solution

Definition of Half-life

Subpart (a)

Subpart (b)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Chemistry Textbooks

Chemistry Branches

The Earths Atmosphere

Nuclear Chemistry

Physical Chemistry

Organic Chemistry

Chemical Reactions

Study anywhere. Anytime. Across all devices.