Certainly! Let's walk through the problem step-by-step to determine which element cesium-135 ([tex]${}_{55}^{135} Cs$[/tex]) becomes after undergoing beta decay.
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### Step-by-Step Solution:
1. Understand Beta Decay:
- In beta decay, a neutron in the nucleus is converted into a proton and an electron (beta particle) is emitted.
- As a result, the atomic number (number of protons) of the element increases by 1, but the mass number (sum of protons and neutrons) remains unchanged because a neutron is lost and a proton is gained.
2. Identify the Initial Element:
- The initial element given is cesium-135 ([tex]${}_{55}^{135} Cs$[/tex]).
- This means cesium (Cs) has an atomic number of 55.
3. Determine the Change in Atomic Number:
- After beta decay, the atomic number increases by 1.
- Therefore, the new atomic number = 55 + 1 = 56.
4. Identify the Resulting Element:
- The element with atomic number 56 is Barium (Ba).
5. Confirm the Mass Number:
- The mass number remains the same during beta decay.
- Therefore, the mass number will still be 135.
6. Resulting Element:
- Combining the new atomic number and the unchanged mass number, the resulting element is [tex]${}_{56}^{135} Ba$[/tex].
Therefore, cesium-135 ([tex]${}_{55}^{135} Cs$[/tex]) becomes barium-135 ([tex]${}_{56}^{135} Ba$[/tex]) after beta decay.
### Conclusion:
- Based on the steps above, the correct answer is:
[tex]\[ \text{D. } {}_{56}^{135} Ba \][/tex]
Thus, after undergoing beta decay, cesium-135 becomes barium-135 ([tex]${}_{56}^{135} Ba$[/tex]).
