Answer :
Let's go through the process of writing the nuclear equation for the beta decay of Cerium-141 step-by-step:
### Step 1: Understand Beta Decay
Beta decay is a type of radioactive decay in which a neutron in the nucleus is converted into a proton and an electron (beta particle) is emitted. As a result:
- The atomic number increases by 1 (because one neutron turns into a proton).
- The mass number remains unchanged (since the total number of nucleons stays the same).
### Step 2: Information About Cerium-141
- Cerium (Ce) has an atomic number of 58.
- The mass number of Cerium-141 is 141.
### Step 3: Determine the Resulting Element
- When Cerium-141 undergoes beta decay, it converts into an element with an atomic number increased by 1.
- The new atomic number will be 58 + 1 = 59.
- The element with atomic number 59 is Praseodymium (Pr).
### Step 4: Write the Nuclear Equation
The nuclear equation for the beta decay of Cerium-141 can be written as follows:
[tex]\[
\overset{141}{58}\text{Ce} \rightarrow \overset{141}{59}\text{Pr} + \overset{0}{-1}\text{e}
\][/tex]
This equation shows that Cerium-141 decays into Praseodymium-141, emitting a beta particle (an electron).
### Final Answer
The nuclear equation for the beta decay of Cerium-141 is:
[tex]\[
\overset{141}{58}\text{Ce} \rightarrow \overset{141}{59}\text{Pr} + \overset{0}{-1}\text{e}
\][/tex]
This equation confirms the transformation of a neutron into a proton within the nucleus of Cerium-141, resulting in the emission of a beta particle and the formation of Praseodymium-141.
### Step 1: Understand Beta Decay
Beta decay is a type of radioactive decay in which a neutron in the nucleus is converted into a proton and an electron (beta particle) is emitted. As a result:
- The atomic number increases by 1 (because one neutron turns into a proton).
- The mass number remains unchanged (since the total number of nucleons stays the same).
### Step 2: Information About Cerium-141
- Cerium (Ce) has an atomic number of 58.
- The mass number of Cerium-141 is 141.
### Step 3: Determine the Resulting Element
- When Cerium-141 undergoes beta decay, it converts into an element with an atomic number increased by 1.
- The new atomic number will be 58 + 1 = 59.
- The element with atomic number 59 is Praseodymium (Pr).
### Step 4: Write the Nuclear Equation
The nuclear equation for the beta decay of Cerium-141 can be written as follows:
[tex]\[
\overset{141}{58}\text{Ce} \rightarrow \overset{141}{59}\text{Pr} + \overset{0}{-1}\text{e}
\][/tex]
This equation shows that Cerium-141 decays into Praseodymium-141, emitting a beta particle (an electron).
### Final Answer
The nuclear equation for the beta decay of Cerium-141 is:
[tex]\[
\overset{141}{58}\text{Ce} \rightarrow \overset{141}{59}\text{Pr} + \overset{0}{-1}\text{e}
\][/tex]
This equation confirms the transformation of a neutron into a proton within the nucleus of Cerium-141, resulting in the emission of a beta particle and the formation of Praseodymium-141.
