QuestionQUESTION ${ }^{\circ}$ ANSWER
In the process of nuclear or radioactive decay, an unstable nucleus spontaneously emits a particle. When this occurs, the nucleus of one element can change into the nucleus of a different element. The resulting change of one element to another is called transmutation. The nuclear decay can be represented by a nuclear equation using atomic symbols for the nuclei and the emitted particles.
Radioactive decay: radioactive nucleus $\rightarrow$ new nucleus + emitted particle
In a nuclear equation, the sum of the mass numbers and the sum of the atomic numbers on one side of the equation must equal the sum of the mass numbers and the sum of the atomic numbers, respectively, on the other side of the equation. ${ }_{19}^{85} \mathrm{~K} \rightarrow-{ }_{-1}^{0} e+{ }_{20}^{38} \mathrm{Ca}$ ${ }_{10}^{3} \mathrm{~K} \rightarrow{ }_{1}^{0} e+{ }_{B}^{3} \mathrm{Ar}$ ${ }_{18}^{3} \mathrm{~K} \rightarrow{ }_{\{ }^{4} \mathrm{He}+{ }_{17}^{4} \mathrm{Cl}$ ${ }_{19}^{38} \mathrm{~K}+{ }_{1}^{0} e \rightarrow{ }_{21}^{38} \mathrm{Ca}$ IDON'T KNOWYET
Identify the balanced nuclear equation for the positron emission of ${ }^{38} \mathbf{K}$ .

Studdy Solution

STEP 1

1. Positron emission involves the conversion of a proton into a neutron, emitting a positron ( $_{+1}^{0}e$ ).
2. The mass number remains the same, but the atomic number decreases by one.
3. We are given several nuclear equations and need to identify the one that represents positron emission of $^{38} \mathrm{K}$ .

STEP 2

1. Understand the process of positron emission.
2. Analyze the given nuclear equations.
3. Identify the correct balanced nuclear equation for the positron emission of $^{38} \mathrm{K}$ .

STEP 3

Positron emission is a type of beta decay where a proton in the nucleus is converted into a neutron, releasing a positron ( $_{+1}^{0}e$ ).

STEP 4

Examine each given nuclear equation to determine if it represents positron emission from $^{38} \mathrm{K}$ .

STEP 5

Analyze the equation: $_{19}^{38} \mathrm{K} \rightarrow _{+1}^{0} e + _{18}^{38} \mathrm{Ar}$
- The mass number remains 38. - The atomic number decreases from 19 to 18, which is consistent with positron emission.

STEP 6

The equation $_{19}^{38} \mathrm{K} \rightarrow _{+1}^{0} e + _{18}^{38} \mathrm{Ar}$ represents the positron emission of $^{38} \mathrm{K}$ .
The balanced nuclear equation for the positron emission of $^{38} \mathrm{K}$ is:
$\boxed{_{19}^{38} \mathrm{K} \rightarrow _{+1}^{0} e + _{18}^{38} \mathrm{Ar}}$

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